diff --git a/ignite/engine/engine.py b/ignite/engine/engine.py
index 2679e97c..22406bad 100644
--- a/ignite/engine/engine.py
+++ b/ignite/engine/engine.py
@@ -695,25 +695,32 @@ class Engine(Serializable):
                     self._setup_engine()
 
                 time_taken = self._run_once_on_dataset()
+                # time is available for handlers but must be update after fire
+                self.state.times[Events.EPOCH_COMPLETED.name] = time_taken
+                handlers_start_time = time.time()
+                if self.should_terminate:
+                    self._fire_event(Events.TERMINATE)
+                else:
+                    self._fire_event(Events.EPOCH_COMPLETED)
+                time_taken += time.time() - handlers_start_time
+                # update time wrt handlers
                 self.state.times[Events.EPOCH_COMPLETED.name] = time_taken
                 hours, mins, secs = _to_hours_mins_secs(time_taken)
-                elapsed_time_message = "Epoch[%s] Complete. Time taken: %02d:%02d:%02d" % (
-                    self.state.epoch,
-                    hours,
-                    mins,
-                    secs,
+                self.logger.info(
+                    "Epoch[%s] Complete. Time taken: %02d:%02d:%02d" % (self.state.epoch, hours, mins, secs)
                 )
                 if self.should_terminate:
-                    self._fire_event(Events.TERMINATE)
-                    self.logger.info(elapsed_time_message)
                     break
-                self._fire_event(Events.EPOCH_COMPLETED)
-                self.logger.info(elapsed_time_message)
 
             time_taken = time.time() - start_time
-            hours, mins, secs = _to_hours_mins_secs(time_taken)
+            # time is available for handlers but must be update after fire
             self.state.times[Events.COMPLETED.name] = time_taken
+            handlers_start_time = time.time()
             self._fire_event(Events.COMPLETED)
+            time_taken += time.time() - handlers_start_time
+            # update time wrt handlers
+            self.state.times[Events.COMPLETED.name] = time_taken
+            hours, mins, secs = _to_hours_mins_secs(time_taken)
             self.logger.info("Engine run complete. Time taken: %02d:%02d:%02d" % (hours, mins, secs))
 
         except BaseException as e:

Epoch Completed and Completed times should include handlers times
## 🚀 Feature

Following discussions here: https://github.com/pytorch/ignite/issues/1098#issuecomment-638170742 idea is to include the times spent in executing handlers attached to `EPOCH_COMPLETED` and `COMPLETED` into https://github.com/pytorch/ignite/blob/93e090ea77f536c1cd50b27ba162adadf64491fc/ignite/engine/engine.py#L699
and 
https://github.com/pytorch/ignite/blob/93e090ea77f536c1cd50b27ba162adadf64491fc/ignite/engine/engine.py#L709



diff --git a/tests/ignite/engine/test_engine.py b/tests/ignite/engine/test_engine.py
index 7c1f0e5d..8c2d966b 100644
--- a/tests/ignite/engine/test_engine.py
+++ b/tests/ignite/engine/test_engine.py
@@ -377,19 +377,29 @@ def test_state_get_event_attrib_value():
 def test_time_stored_in_state():
     def _test(data, max_epochs, epoch_length):
         sleep_time = 0.01
+        extra_sleep_time = 0.1
         engine = Engine(lambda e, b: time.sleep(sleep_time))
 
-        def check_epoch_time(engine):
+        @engine.on(Events.EPOCH_COMPLETED)
+        def check_epoch_time():
             assert engine.state.times[Events.EPOCH_COMPLETED.name] >= sleep_time * epoch_length
+            time.sleep(extra_sleep_time)
 
-        def check_completed_time(engine):
-            assert engine.state.times[Events.COMPLETED.name] >= sleep_time * epoch_length * max_epochs
-
-        engine.add_event_handler(Events.EPOCH_COMPLETED, lambda e: check_epoch_time(e))
-        engine.add_event_handler(Events.COMPLETED, lambda e: check_completed_time(e))
+        @engine.on(Events.COMPLETED)
+        def check_completed_time():
+            assert (
+                engine.state.times[Events.COMPLETED.name] >= (sleep_time * epoch_length + extra_sleep_time) * max_epochs
+            )
+            time.sleep(extra_sleep_time)
 
         engine.run(data, max_epochs=max_epochs, epoch_length=epoch_length)
 
+        assert engine.state.times[Events.EPOCH_COMPLETED.name] >= sleep_time * epoch_length + extra_sleep_time
+        assert (
+            engine.state.times[Events.COMPLETED.name]
+            >= (sleep_time * epoch_length + extra_sleep_time) * max_epochs + extra_sleep_time
+        )
+
     _test(list(range(100)), max_epochs=2, epoch_length=100)
     _test(list(range(200)), max_epochs=2, epoch_length=100)
     _test(list(range(200)), max_epochs=5, epoch_length=100)

pip install -e .
parse_log_pytest
requirements.txt
pytest
apt-get update apt-get install -y gcc pip install torch torchvision -f https://download.pytorch.org/whl/cpu/torch_stable.html -U
3.7
requirements-dev.txt
pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
absl-py==2.1.0
alembic==1.12.1
arrow==1.2.3
attrs==24.2.0
boto3==1.33.13
botocore==1.33.13
bravado==11.1.0
bravado-core==6.1.1
cached-property==1.5.2
cachetools==5.5.2
certifi @ file:///croot/certifi_1671487769961/work/certifi
charset-normalizer==3.4.1
click==7.1.2
cloudpickle==2.2.1
codecov==2.1.13
coverage==7.2.7
cycler==0.11.0
databricks-cli==0.18.0
dill==0.3.7
docker==6.1.3
docker-pycreds==0.4.0
entrypoints==0.4
exceptiongroup==1.2.2
execnet==2.0.2
Flask==1.1.4
fonttools==4.38.0
fqdn==1.5.1
funcsigs==1.0.2
furl==2.1.4
future==1.0.0
gitdb==4.0.12
GitPython==3.1.44
google-auth==2.38.0
google-auth-oauthlib==0.4.6
greenlet==3.1.1
grpcio==1.62.3
gunicorn==20.1.0
gym==0.26.2
gym-notices==0.0.8
hestia==0.6.0
humanfriendly==10.0
idna==3.10
importlib-metadata==5.2.0
importlib-resources==5.12.0
iniconfig==2.0.0
isoduration==20.11.0
itsdangerous==1.1.0
Jinja2==2.10.3
jmespath==1.0.1
joblib==1.3.2
jsonpatch==1.33
jsonpointer==3.0.0
jsonref==1.1.0
jsonschema==4.17.3
kiwisolver==1.4.5
Mako==1.2.4
Markdown==3.4.4
MarkupSafe==2.1.5
marshmallow==3.0.0rc5
matplotlib==3.5.3
mlflow==1.30.1
monotonic==1.6
msgpack==1.0.5
neptune-client==1.11.1
networkx==2.6.3
numpy==1.21.6
oauthlib==3.2.2
orderedmultidict==1.0.1
packaging==21.3
pandas==1.3.5
pathlib2==2.3.7.post1
Pillow==9.5.0
pkgutil_resolve_name==1.3.10
platformdirs==4.0.0
pluggy==1.2.0
polyaxon-client==0.6.1
polyaxon-schemas==0.6.1
polystores==0.2.5
prometheus-client==0.17.1
prometheus_flask_exporter==0.23.2
protobuf==3.20.3
psutil==7.0.0
pyasn1==0.5.1
pyasn1-modules==0.3.0
PyJWT==2.8.0
pynvml==11.5.3
pyparsing==3.1.4
pyrsistent==0.19.3
pytest==7.4.4
pytest-cov==4.1.0
pytest-xdist==3.5.0
python-dateutil==2.9.0.post0
-e git+https://github.com/pytorch/ignite.git@b9f3467d8935bbaa4e68363c0a7f0f7dbb5edcef#egg=pytorch_ignite
pytz==2022.7.1
PyYAML==6.0.1
querystring-parser==1.2.4
requests==2.31.0
requests-file==2.1.0
requests-oauthlib==2.0.0
requests-toolbelt==1.0.0
rfc3339-validator==0.1.4
rfc3986-validator==0.1.1
rhea==0.5.5
rsa==4.9
s3transfer==0.8.2
scikit-learn==1.0.2
scipy==1.7.3
sentry-sdk==2.24.1
setproctitle==1.3.3
simplejson==3.20.1
six==1.17.0
smmap==5.0.2
SQLAlchemy==1.4.54
sqlparse==0.4.4
swagger-spec-validator==3.0.3
tabulate==0.9.0
tensorboard==2.11.2
tensorboard-data-server==0.6.1
tensorboard-plugin-wit==1.8.1
tensorboardX==2.6.2.2
threadpoolctl==3.1.0
tomli==2.0.1
torch==1.13.1+cpu
torchvision==0.14.1+cpu
tornado==6.2
tqdm==4.67.1
trains==0.16.4
typing_extensions==4.7.1
uri-template==1.3.0
urllib3==1.26.20
visdom==0.2.4
wandb==0.18.7
webcolors==1.13
websocket-client==1.6.1
Werkzeug==1.0.1
zipp==3.15.0

name: ignite
channels:
  - defaults
  - https://repo.anaconda.com/pkgs/main
  - https://repo.anaconda.com/pkgs/r
  - conda-forge
dependencies:
  - _libgcc_mutex=0.1=main
  - _openmp_mutex=5.1=1_gnu
  - ca-certificates=2025.2.25=h06a4308_0
  - certifi=2022.12.7=py37h06a4308_0
  - ld_impl_linux-64=2.40=h12ee557_0
  - libffi=3.4.4=h6a678d5_1
  - libgcc-ng=11.2.0=h1234567_1
  - libgomp=11.2.0=h1234567_1
  - libstdcxx-ng=11.2.0=h1234567_1
  - ncurses=6.4=h6a678d5_0
  - openssl=1.1.1w=h7f8727e_0
  - pip=22.3.1=py37h06a4308_0
  - python=3.7.16=h7a1cb2a_0
  - readline=8.2=h5eee18b_0
  - setuptools=65.6.3=py37h06a4308_0
  - sqlite=3.45.3=h5eee18b_0
  - tk=8.6.14=h39e8969_0
  - wheel=0.38.4=py37h06a4308_0
  - xz=5.6.4=h5eee18b_1
  - zlib=1.2.13=h5eee18b_1
  - pip:
      - absl-py==2.1.0
      - alembic==1.12.1
      - arrow==1.2.3
      - attrs==24.2.0
      - boto3==1.33.13
      - botocore==1.33.13
      - bravado==11.1.0
      - bravado-core==6.1.1
      - cached-property==1.5.2
      - cachetools==5.5.2
      - charset-normalizer==3.4.1
      - click==7.1.2
      - cloudpickle==2.2.1
      - codecov==2.1.13
      - coverage==7.2.7
      - cycler==0.11.0
      - databricks-cli==0.18.0
      - dill==0.3.7
      - docker==6.1.3
      - docker-pycreds==0.4.0
      - entrypoints==0.4
      - exceptiongroup==1.2.2
      - execnet==2.0.2
      - flask==1.1.4
      - fonttools==4.38.0
      - fqdn==1.5.1
      - funcsigs==1.0.2
      - furl==2.1.4
      - future==1.0.0
      - gitdb==4.0.12
      - gitpython==3.1.44
      - google-auth==2.38.0
      - google-auth-oauthlib==0.4.6
      - greenlet==3.1.1
      - grpcio==1.62.3
      - gunicorn==20.1.0
      - gym==0.26.2
      - gym-notices==0.0.8
      - hestia==0.6.0
      - humanfriendly==10.0
      - idna==3.10
      - importlib-metadata==5.2.0
      - importlib-resources==5.12.0
      - iniconfig==2.0.0
      - isoduration==20.11.0
      - itsdangerous==1.1.0
      - jinja2==2.10.3
      - jmespath==1.0.1
      - joblib==1.3.2
      - jsonpatch==1.33
      - jsonpointer==3.0.0
      - jsonref==1.1.0
      - jsonschema==4.17.3
      - kiwisolver==1.4.5
      - mako==1.2.4
      - markdown==3.4.4
      - markupsafe==2.1.5
      - marshmallow==3.0.0rc5
      - matplotlib==3.5.3
      - mlflow==1.30.1
      - monotonic==1.6
      - msgpack==1.0.5
      - neptune-client==1.11.1
      - networkx==2.6.3
      - numpy==1.21.6
      - oauthlib==3.2.2
      - orderedmultidict==1.0.1
      - packaging==21.3
      - pandas==1.3.5
      - pathlib2==2.3.7.post1
      - pillow==9.5.0
      - pkgutil-resolve-name==1.3.10
      - platformdirs==4.0.0
      - pluggy==1.2.0
      - polyaxon-client==0.6.1
      - polyaxon-schemas==0.6.1
      - polystores==0.2.5
      - prometheus-client==0.17.1
      - prometheus-flask-exporter==0.23.2
      - protobuf==3.20.3
      - psutil==7.0.0
      - pyasn1==0.5.1
      - pyasn1-modules==0.3.0
      - pyjwt==2.8.0
      - pynvml==11.5.3
      - pyparsing==3.1.4
      - pyrsistent==0.19.3
      - pytest==7.4.4
      - pytest-cov==4.1.0
      - pytest-xdist==3.5.0
      - python-dateutil==2.9.0.post0
      - pytorch-ignite==0.5.0
      - pytz==2022.7.1
      - pyyaml==6.0.1
      - querystring-parser==1.2.4
      - requests==2.31.0
      - requests-file==2.1.0
      - requests-oauthlib==2.0.0
      - requests-toolbelt==1.0.0
      - rfc3339-validator==0.1.4
      - rfc3986-validator==0.1.1
      - rhea==0.5.5
      - rsa==4.9
      - s3transfer==0.8.2
      - scikit-learn==1.0.2
      - scipy==1.7.3
      - sentry-sdk==2.24.1
      - setproctitle==1.3.3
      - simplejson==3.20.1
      - six==1.17.0
      - smmap==5.0.2
      - sqlalchemy==1.4.54
      - sqlparse==0.4.4
      - swagger-spec-validator==3.0.3
      - tabulate==0.9.0
      - tensorboard==2.11.2
      - tensorboard-data-server==0.6.1
      - tensorboard-plugin-wit==1.8.1
      - tensorboardx==2.6.2.2
      - threadpoolctl==3.1.0
      - tomli==2.0.1
      - torch==1.13.1+cpu
      - torchvision==0.14.1+cpu
      - tornado==6.2
      - tqdm==4.67.1
      - trains==0.16.4
      - typing-extensions==4.7.1
      - uri-template==1.3.0
      - urllib3==1.26.20
      - visdom==0.2.4
      - wandb==0.18.7
      - webcolors==1.13
      - websocket-client==1.6.1
      - werkzeug==1.0.1
      - zipp==3.15.0
prefix: /opt/conda/envs/ignite

tests/ignite/engine/test_engine.py::test_time_stored_in_state
tests/ignite/engine/test_engine.py::test_terminate tests/ignite/engine/test_engine.py::test_invalid_process_raises_with_invalid_signature tests/ignite/engine/test_engine.py::test_current_epoch_counter_increases_every_epoch tests/ignite/engine/test_engine.py::test_current_iteration_counter_increases_every_iteration tests/ignite/engine/test_engine.py::test_stopping_criterion_is_max_epochs tests/ignite/engine/test_engine.py::test_terminate_at_end_of_epoch_stops_run tests/ignite/engine/test_engine.py::test_terminate_at_start_of_epoch_stops_run_after_completing_iteration tests/ignite/engine/test_engine.py::test_terminate_stops_run_mid_epoch tests/ignite/engine/test_engine.py::test_terminate_epoch_stops_mid_epoch tests/ignite/engine/test_engine.py::test_iteration_events_are_fired tests/ignite/engine/test_engine.py::test_last_event_name tests/ignite/engine/test_engine.py::test_reset_should_terminate tests/ignite/engine/test_engine.py::test_batch_values tests/ignite/engine/test_engine.py::test_state_repr tests/ignite/engine/test_engine.py::test_alter_batch tests/ignite/engine/test_engine.py::test__is_done tests/ignite/engine/test_engine.py::test__setup_engine tests/ignite/engine/test_engine.py::test_run_asserts tests/ignite/engine/test_engine.py::test_state_get_event_attrib_value tests/ignite/engine/test_engine.py::test_run_check_triggered_events_list tests/ignite/engine/test_engine.py::test_run_check_triggered_events_on_iterator tests/ignite/engine/test_engine.py::test_distrib_cpu tests/ignite/engine/test_engine.py::test_engine_random_state tests/ignite/engine/test_engine.py::test_altered_random_state tests/ignite/engine/test_engine.py::test_engine_with_dataloader_no_auto_batching tests/ignite/engine/test_engine.py::test_run_once_finite_iterator_no_epoch_length tests/ignite/engine/test_engine.py::test_run_finite_iterator_no_epoch_length tests/ignite/engine/test_engine.py::test_run_finite_iterator_no_epoch_length_2 tests/ignite/engine/test_engine.py::test_faq_inf_iterator_with_epoch_length tests/ignite/engine/test_engine.py::test_faq_inf_iterator_no_epoch_length tests/ignite/engine/test_engine.py::test_faq_fin_iterator_unknw_size tests/ignite/engine/test_engine.py::test_faq_fin_iterator tests/ignite/engine/test_engine.py::test_set_data
ignite/engine/engine.py
ignite/engine/engine.py