The offer price of 305 pence per share represents a premium of 11.2 percent to Brit's closing price on Feb. 16.
Investor Prem Watsa-led Fairfax said it has received hard irrevocable undertakings to accept the offer from entities managed by Apollo Global and CVC Capital Partners, which together hold about 73 percent of Brit's issued share capital.
Apollo and CVC, which acquired Netherlands-based Brit in 2010, sold about 25 percent of the company, launching it on the London stock exchange last year and valuing it up to 960 million pounds ($1.48 billion).
Brit underwrites a broad class of commercial specialty insurance with a strong focus on property, casualty and energy business.
"Brit has an outstanding track record over the last ten years and will continue to operate on a decentralized basis once owned by Fairfax," said Fairfax Chief Executive Prem Watsa.
The acquisition is accretive to Fairfax on several metrics, including gross revenue per share and investments per share, the company said in a statement.
Earlier this month, Toronto-based Fairfax Financial Holdings agreed to acquire the Ukrainian insurance operations of Australia's QBE Insurance Group, expanding its presence in Eastern Europe.