The deal is about 290 million US dollars and will be sold to private equity firms Blackstone and TPG, as part of a plan to offload non-core assets.
Investec bought Kensington, which had specialised in lending to home buyers with poor credit histories, in a 283 million pound deal in 2007 - just before the global economic crisis sent a judder through the housing market in Britain and Ireland, where many of its assets were located.
Since then Kensington has changed its focus to safer "prime" lending, but has been dogged by a sharp fall in property prices in Ireland, one of the biggest casualties of the euro zone financial crisis. Investec has been forced to take substantial impairment charges for its losses there.
The sale of Kensington, which follows that of Investec's struggling Australian professional finance and leasing arm in April, does not include the Irish operations, Investec said.
Blackstone and TPG said in a statement they intend to develop Kensington's mortgage lending business and broader speciality finance capabilities.
Fenchurch and Investec investment banking unit were the advisors to Investec.