The agreement comes less than a year after Brit, which is based in London, went public in an offering that valued the firm around 960 million pounds, or about $1.6 billion using the exchange rate at the time.
Brit is a member of the Lloyd's of London insurance market, in which syndicates of specialist companies join together to share the risk in underwriting policies. The Lloyd's marketplace wrote the first aviation insurance policy, insured Betty Grable's legs and provided coverage for a 69-carat diamond that the actor Richard Burton bought for Elizabeth Taylor.
The deal is expected to expand Fairfax's presence in the Lloyd's marketplace, complement Fairfax's existing operations and help diversify its risk portfolio.
Under the terms of the offer, investors would receive £3.05 in cash for each share of Brit they hold, including the company's final dividend for the year ended Dec. 31, 2014. The offer represents an 11.2 percent premium to Brit's closing price on Monday.
Shares of Brit rose 10 percent to £3.02 in early trading in London on Tuesday.
"Brit has an outstanding track record over the last 10 years and will continue to operate on a decentralized basis once owned by Fairfax," Prem Watsa, Fairfax's chairman and chief executive, said in a news release late Monday. "With the acquisition of Brit, Fairfax will have a significant top five position at Lloyd's of London."
Brit was acquired by the private equity firms Apollo Global Management and CVC Capital Partners in 2010. Apollo and CVC sold about 25 percent of the firm in an initial public offering last March.
As part of the Fairfax deal, entities managed by Apollo and CVC have agreed to irrevocable undertakings to accept the offer. Those entities hold a combined stake of about 73 percent of Brit's shares.
The transaction is subject to regulatory approval.
"Brit's board is pleased to recommend the combination with Fairfax, which I believe will bring us significantly closer to realizing our strategy of building the leading global speciality (re)insurer," Richard Ward, Brit's chairman, said on Tuesday in a news release. "Our two businesses are highly complementary and the proposed deal provides both groups with an exciting opportunity to deliver our respective growth ambitions."
After it was acquired by Apollo and CVC, Brit sold several business lines, including its general insurance business in Britain to a Fairfax unit in 2012.
It now focuses on specialty insurance and reinsurance for businesses and has a large presence in the Lloyd's of London marketplace. The company had gross written premiums of £1.19 billion in 2013.
Founded in 1985, Fairfax, based in Toronto, offers property and casualty insurance, reinsurance and investment management services. The company had gross written premiums of $7.22 billion in 2013.
Shares of Fairfax closed 1.1 percent higher at 642 Canadian dollars in Toronto on Monday.