How can I do tree_method ='exact' in XGBoost classifier?
Indeed tree_method is a parameter for Tree Booster. There are 4 choices, namely, auto, exact, approx and hist. The default is set to auto which  heuristically chooses a faster algorithm based on the size of your dataset. Approximate algorithm (approx) is chosen in your case since your dataset is huge. 

To change the tree construction algorithm, you have to pass tree_method in the train function as follows:

import xgboost as xgb
...
parameters = {'tree_method': 'exact'} #You can add other parameters as well
model = xgb.train(parameters, x_train, num_round) #num_round is the number of rounds for boosting
prediction = model.predict(x_test)
...


I hope this helps.