The firm accused of incorrectly withdrawing tax credits from hundreds of claimants is to have its contract ended early, staff have been told.
Work being done by Concentrix will be brought back in-house immediately rather than waiting for the end of the contract next year, said the Public and Commercial Service union (PCS).
HM Revenue and Customs announced last month it would not extend its contract with the company, which was at the centre of a parliamentary debate earlier this week.
MPs heard from Sarah Broome, a 40-year-old single mother from West Molesey in Surrey, who claimed she was forced to go six weeks out of pocket due to a decision by the company to end her payments.
PCS general secretary Mark Serwotka said: "We're delighted HMRC has agreed with us this work is best carried out in-house and, crucially, has accepted our argument to protect the jobs of Concentrix staff by transferring them into the department. We will be pushing for these workers to be employed on the same terms as their HMRC colleagues.
"Sadly, this could all have been avoided and the fiasco is further evidence it is a false economy to hive off important public services."
A staff bulletin said discussions were continuing about the remaining period of the contract, adding that Belfast-based staff will automatically transfer to HMRC.
"This will provide permanent employment to Concentrix people who we require to deliver our priorities, offering job security to them well beyond the scheduled expiry of the contract in May 2017.
"We are currently working to agree transfer dates but it will be in the next few weeks."
Rebecca Long-Bailey, shadow chief secretary to the Treasury, said: "This is a great victory for those families who have been unfairly targeted by Concentrix and for Labour and the trade unions, who have mounted immense pressure on the Tory Government to bring this operation back in house.
"I am pleased to hear that Concentrix employees will not be losing their jobs as a result of their company's and this Government's failures and will simply be transferred to HMRC.
"However, this Government still has a lot of questions to answer about how this mess came about in the first place and why they were so slow to take action. Labour will be holding a debate in Parliament next week calling for an immediate investigation into the Government's handling of the contract and for urgent action to compensate families who have unjustly had their tax credits stripped away."
A Concentrix spokesman said: "As the work previously carried out by Concentrix moves back to HMRC this means that, under the protection of employment regulations, Concentrix staff carrying out the work for HMRC will automatically transfer to HMRC.
"We have begun discussions with the staff about this transfer. This will provide permanent employment, offering job security to them well beyond the scheduled expiry of the contract in May 2017. We do not expect any forced redundancies as a result of this transfer."
A HMRC spokesman added: "Concentrix has begun discussions with their staff about this transfer. Those people moving to HMRC will be supported through further training, building on the improvements already delivered to the service we provide to our tax credits customers."