The call handling and IT system is more than Â£40m over budget and was initially due to be ready for October 2013.
An earlier attempt to introduce the system had to be abandoned.
The programme will now be phased in for some services from this summer with a national roll-out by the end of 2017.
Earlier this year, the planned June launch was pushed back to the "summer of 2016" after an issue that caused computer screens to appear blank.
It followed an earlier incident in which the system crashed and staff had to resort to pen and paper to deal with patient calls.
The new technology is meant to make NHS 24 more efficient but is expected to cost Â£117m, more than 50% higher than the original estimate.
NHS 24 said the new telephone system would be in place this year for services including Breathing Space, NHS Living Life, the musculoskeletal helpline, death certification, blood transfusion and Fit For Work.
It will then be introduced in one health board area to ensure it is working effectively before the national roll-out.
NHS 24 chief executive Angiolina Foster said: "We expect to have a functioning technology system tested and available later in the summer.
"However, we have recognised that ensuring our staff and operational environment are also fully ready to accept the technology is absolutely essential to making sure we can make a smooth transition to the new system."
Ms Foster said: "We recognise that the past 18 months have been challenging for the organisation and know that the professionalism and dedication of our people has enabled us to give high-quality care to patients during this time."
Health Secretary Shona Robison said: "While any delays to implementation are disappointing, patient safety must always come first. This is why NHS 24 has taken the decision to phase the roll-out of its Future Programme.
"This decision follows a comprehensive review of the new system which concluded that a phased roll-out later this summer, working towards full implementation across all health boards by the end of 2017, would be both safe for patients and deliverable by the organisation."
A crisis-hit computer project for the NHS 24 telephone helpline will not be fully rolled out across Scotland until the end of next year - four years later than originally planned.