Yorkshire, owned by its customers, said the Egg businesses it was acquiring comprised of a £2.5bn savings book and a 430 million pound mortgage book. It added it would also acquire the Egg brand.
The sale of the Egg divisions to Yorkshire Building Society comes just a few months after Citi had sold off Egg's credit card assets to Barclays.
Yorkshire Building Society, which has more than £30bn worth of assets, said buying the Egg businesses would widen its products and range of services, and improve the company's funding position.
Yorkshire did not disclose how much it paid for the Egg businesses.
Yorkshire Building Society is also looking at Northern Rock, the fully nationalised bank which the government aims to sell off in due course.
Citi acquired Egg from insurer Prudential in 2007 for £575m and the American bank had been looking to sell Egg for some time.