The UK's oldest general insurer, which first announced the approach almost a fortnight ago, recommended shareholders accept the all-cash offer from Canada's Intact Financial and Tryg of Denmark.
If successful, it will be the biggest overseas takeover of a British company this year.
The foreign suitors would carve up RSA, with Intact keeping its Canada, UK and international operations while Tryg would take control of its Sweden and Norway businesses.
The pair would co-own RSA's Danish unit.
Tryg would pay £4.2bn while Intact would contribute £3bn.
It will see the companies pay 685p a share, as well as an 8p a share dividend payout.
The price represents a 51% premium to RSA's closing share price of 460p on 4 November when the offer was made.
Shareholders reacted with glee to the disclosure at that time following years of below-average returns though current chief executive Stephen Hester, who led the post-crisis recovery of RBS, was credited with turning a corner since joining in 2014 through cutting under-performing operations.
He confirmed he would leave the business on completion of the deal which, he expected, would result in a small number of job losses at its UK HQ - the so-called Walkie Talkie building in the City.
Activist investor and RSA's largest shareholder Cevian Capital said it fully supported the takeover.
Its co-founder Christer Gardell responded: "We assess that the long-term competitiveness of RSA's business will benefit from combining with Tryg and Intact, the best-performing non-life companies in their respective geographies."
Tryg CEO Morten Hubbe said of the deal: "Our deep knowledge of these markets makes us ideally placed to integrate, operate and enhance the value of our combined group over the long term."