Aviva said the addition of RAC's brand and customer base would boost its general insurance business, which insures one-in-seven of all UK motor vehicles.
The proposed deal, which has the backing of the RAC board, came after a day of speculation that a bid was in the pipeline for the 108-year-old business.
The RAC's portfolio of businesses ranges from the BSM driving school to travel insurance and financial services, as well as roadside recovery.
It has about 275,000 motor and home policyholders under the RAC Insure brand, while its business services arm includes Lex Vehicle Leasing - a joint venture with HBOS offering contract hire, fleet management and car finance services.
The move comes less than a year after rival the AA was bought by a private equity consortium for £1.75billion.
The RAC was a private members' club for nearly a century until it was bought by listed car hire company Lex for £437million in 1999, resulting in £34,000 windfalls for its 12,000 full time members.