Resolution said it would be investing £140m over four years to consolidate its customer services and IT operations, which are currently based in Glasgow and Birmingham.
Under the partnership, about 2,000 Resolution staff are to transfer to Capita by August.
It also aims to move a number of its key back-office functions to India.
The company said: “As work is transferred offshore, Capita is confident that, with natural staff turnover and a significant proportion of staff being redeployed within its existing UK operations, there would be less than 500 redundancies over a three-year period.”
All customer-facing roles will remain in the UK, as will customer data.