The 15-year contract will see the companies become the West Midlands authority’s partner, delivering a range of support services including HR, customer services, finance and IT.
About 60 HR staff will transfer to the new partnership, on the same pay and conditions, but eventually moving to a new regional business centre.
Deputy leader Pauline Hinton said there would be no compulsory redundancies as a result of the deal.
“It’s a straight transfer and no job cuts,” she said.
A handful of people will remain in the corporate HR function to run “the strategic side” of the council’s work.
Unions were angered at the prospect of council jobs being switched to the private sector, but Hinton said the HR team would continue to work on council services.
“There were staff concerns when the council started the process, so we set up a series of meetings with both staff and unions,” she said.
BT and Liberata will invest £45m to upgrade the council’s IT infrastructure and computer systems.
It is estimated the partnership will also achieve an additional £57m of efficiency savings over the contract life through procurement and other business process streamlining.
Mark Quartermaine, managing director for government services at BT, said: “Councils face major challenges over the next few years and this announcement demonstrates how local authorities can tap into private sector expertise.”