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."

Mr Byrne was shot dead in the Regency Hotel during a boxing weigh-in in the north of the city in February.
This is the second search to be carried out in a week.
RTÉ has reported that searches are being carried out on ten houses and flats in Dublin's south inner city.
The operation began at around 06:30 local time on Friday morning.
It is understood that over 80 armed gardaí are involved in the investigation, as well as the Emergency Response Unit, the Drugs and Organised Crime unit and the Criminal Asset Bureau.
On Wednesday, Irish authorities seized over 1m euros (£770,000) worth of luxury cars, cash and other valuables.

Jacqui Thompson was arrested in 2011 for filming a Carmarthenshire council meeting and sued Mark James for libel.
He counter-sued for posts made on her blog and received £25,000 in damages.
The Crown Prosecution Service (CPS) said Mrs Thompson had been charged with an harassment offence but a decision was taken to discontinue her case.
Mrs Thompson, of Llanwrda, said she was "relieved" at the news and had been worried about her impending court case, which was due to take place on Thursday.
A CPS spokesman said: "Following a review, prosecutors were no longer satisfied there was a realistic prospect of conviction due to insufficient evidence and therefore made the decision to discontinue the case."
Mrs Thompson became embroiled in the legal row after she was arrested in June 2011 for refusing to stop filming a council meeting for her blog, in which she was critical of the authority.
She sued Mr James the following November and he successfully counter-sued in a private lawsuit.
In 2016, the High Court found Mrs Thompson had run a campaign of "harassment, defamation and intimidation" against Mr James.
She was told to pay back £250 a month to him over the next 10 years to cover the damages.
Carmarthenshire council covered Mr James' legal costs, a decision the Wales Audit Office later found to be unlawful.
But the authority is pursuing Mrs Thompson for £190,393 in legal costs.
The council would not comment on the latest development in the case, which it said was a private matter for Mr James.
Mr James has been asked to comment.
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.
[NEXT_CONCEPT]
Irish police have begun another series of raids on properties linked to members of a criminal gang connected to shooting victim David Byrne in Dublin.
[NEXT_CONCEPT]
A blogger who launched a "campaign of harassment" against a council chief executive has had the criminal case against her dropped.