Intact said the deal would lead to some job cuts in RSA’s global head office functions as it looks to axe some duplication, but did not provide figures.
RSA employs around 13,500 employees worldwide and has about nine million customers across more than 100 countries.
Tryg said it was likely to cut between 10pc and 15pc of staff in the combined businesses across Norway and Sweden in the first three years following the acquisition.
The sale will be put to RSA shareholders, with 15pc of its investors already pledging to back the takeover.
Martin Scicluna, chairman of RSA, 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.”
For Intact, which already has more than 16,000 staff, the deal will mark its debut into the UK market and mark a “significant step to accelerate its strategy and leadership”.
RSA – which underwrites home and pet insurance offered by the likes of John Lewis, Tesco and Argos – traces its roots back more than three centuries to the original Sun Insurance company set up in 1706 by entrepreneur Charles Povey to protect livelihoods after the Great Fire of London.
RSA shares rose nearly 4pc in morning trade to 671.70p.