O’Sullivan has held roles at Bank of America, Goldman, Barclays, Man Group and Collins Stewart.
He has been chairman of Old Mutual since January 2010. He will keep that job until Old Mutual has completed the separation of its wealth management and emerging markets business, which should be by the end of this year.
O’Sullivan said: “Saga is a household name and a brand that I admire. I am very pleased to be joining at a pivotal moment.”