Bank of Montreal, Canada’s fourth-biggest bank, agreed to buy Marshall & Ilsley Corp. for about $4.1 billion in stock to double its U.S. deposits and branches.

Bank of Montreal will pay 0.1257 of its own share for each share of M&I, the Toronto-based bank said Friday in a statement. The deal values M&I at $7.75 a share, 34 percent higher than Thurday’s closing price of $5.79 on the New York Stock Exchange.

With the purchase of the Milwaukee-based company, Bank of Montreal more than doubles its U.S. branches to 695, and increases its U.S. assets to $162 billion. Marshall & Ilsley has outlets in states including Indiana, Minnesota, Missouri, Kansas and Wisconsin.

The acquisition “transforms BMO’s competitive position in the U.S.,” said Bill Downe, CEO of BMO Financial Group.

M&I has about 30 branches in the Indianapolis area and controls about 6 percent of the market's bank deposits, according to the Federal Deposit Insurance Corp. The bank had nearly $1.8 billion in local deposits as of June 30. It is ranked sixth among area banks in terms of employment, with about 400 workers.

M&I entered the Indianapolis market in 2008 when it acquired First Indiana Corp. for about $529 million.

Bank of Montreal also is the parent bank of Harris Bank, which has about 10 branches and 100 employees in Indianapolis.

Canadian banks, ranked the world’s soundest for three straight years by the World Economic Forum, have been expanding in the U.S., where companies faltered as the real-estate market tumbled. M&I has posted eight straight quarterly losses while Bank of Montreal has reported six consecutive quarters of profit growth, a streak unmatched by Canada’s five other large lenders.

Bank of Montreal will raise about $794 million in shares to help finance the purchase, the largest takeover ever for the Canadian bank. The deal will add to earnings in 2013, excluding merger costs of $536 million.