State-backed RBS put around 200 million pounds worth of Channel Island assets up for sale in October in order to comply with new ring-fencing rules coming into force in 2019.
The rules require UK banks to separate retail operations from other riskier businesses such as investment banking to protect depositors money.
Together, Investec and Shawbrook will take over the loans, which were provided to businesses to buy assets such as machinery, ships or aircraft.
"This is part of our long-term strategy to increase the specialist finance services we can provide to our clients," the Investec spokesman said.
Sky News, which first reported the deal, said it was worth around 150 million pounds.
RBS declined to comment.
(Editing by Jason Neely and Elaine Hardcastle)
By Emma Rumney