However, the termination of long-term interest rate swaps on the remaining mortgage portfolio will result in a net loss over the two transactions.
The mortgages were acquired by UKAR during the financial crisis and were formerly owned by Bradford & Bingley and NRAM Limited, which was part of Northern Rock.
A statement from UKAR said the assets will be sold for a price above their book value with proceeds being used to pay down the national debt.
“However, given the unwinding of the swaps, national debt will be reduced by an amount which is less than the sale proceeds,” it added.
The exact figure will be known when the transaction completes in the next few weeks and will subsequently be disclosed to Parliament.
Following the transaction UKAR owns around £13bn worth of assets, down from £21bn in September 2017 and from £116bn in 2010.
Rothesay Life is regulated by the Financial Conduct Authority and Prudential Regulation Authority.
There will be no changes to the terms and conditions of the mortgages sold and borrowers do not need to take any action.
The interest rate swaps hedge the risk of changes in interest rates held against these mortgages.
“These swaps were taken out by Bradford & Bingley and Northern Rock more than 10 years ago when the loans were issued, in line with good risk management practice,” UKAR said.
“Due to the fall in long term interest rates, there is a substantial cost for terminating the swaps which is expected to exceed the profit on the sale of the loans, resulting in a net overall accounting loss on the two transactions,” it added.
Chancellor Philip Hammond (pictured) said: “We’re continuing to recover the money the taxpayer committed during the financial crash, and the sale of these loans moves us one step closer.
“As a result of this transaction UKAR expects to repay approximately £1bn of the government loan which is made up of a number of components in addition to the actual sales proceeds.
“Following repayment, UKAR will have repaid 94% of its loans from the government,” he added.