The all-cash offer for the FTSE100 company will involve Intact Financial Corporation of Canada and Tryg, a Danish insurer.
The deal will see RSA’s global operations broken up and significant restructuring and reorganisation.
RSA runs the MoreThan car insurer in the UK and has subsidiaries in several countries throughout the world.
Intact and Trygg will separate the businesses as part of the deal.
If the deal is accepted by shareholders Intact will take control of the company’s UK, Canadian, and international operations with Tryg taking over most of the Scandinavian business.
The offer price equates to 685p a share, about 50% higher than RSA’s share price before the bid.
RSA chairman Martin Scicluna said the deal was a good one for shareholders.
He said: "The board of RSA is pleased to be recommending Intact and Tryg's cash offer for the company, which delivers attractive, certain value for our shareholders. The offer reflects the strength and performance of RSA during a challenging period for our industry, representing a significant premium in cash. We believe that our staff, our businesses and our customers can prosper under the stewardship of Intact and Tryg, two great businesses with long histories and strong reputations."
"RSA has provided peace of mind to individuals and protected businesses from risk for more than 300 years. That history has seen significant consolidation in the insurance industry, a process that continues today. However, I am confident that the values of our business, and not least our dedication to serving customers well, will be sustained as part of Intact and Tryg."
Tryg will pay £4.2bn for its chunk of the business with Intact will pay £3bn.
Charles Brindamour, CEO of Intact, said: "This Transaction is highly strategic for Intact and today we have reached an important milestone. Acquiring RSA's strong businesses will expand our leadership position in Canada, build on our expertise in specialty lines, and provide a substantial opportunity to build on the UK and international operations."