Fairfax says the purchase will give it a significant presence in the Lloyds of London market.
Under the terms of the Fairfax offer, Brit shareholders will receive 305 pence in cash per share, including any final dividend for the year ended December 31, 2014.
The Brit offer price represents a premium of 11.2 per cent to the closing price of 274.2 pence per Brit share on Monday.
Fairfax says it has built a strong relationship with the Brit team and an understanding of their business and operations since the acquisition of Brit's runoff business in June, 2012.
"Brit has an outstanding track record over the last ten years and will continue to operate on a decentralized basis once owned by Fairfax," Prem Watsa , chairman and CEO of Fairfax, said in a statement.
"With the acquisition of Brit, Fairfax will have a significant top five position at Lloyds of London."
The Fairfax offer to buy Brit is subject to customary closing conditions, including customary competition and merger conditions.