Bank of Montreal will acquire Marshall & Ilsley Corp. in a stock-for-stock deal valued at about $4.1 billion, further strengthening the Canadian bank’s position in the Midwest.

Bank of Montreal said Friday that, under the definitive agreement, it’s offering 0.1257 of a share for each M&I share. Based on Bank of Montreal’s closing stock price in Toronto Thursday, the deal values M&I at $7.75 a share.

Earlier this year, Bank of Montreal bought Rockford-based Amcore Bank NA in a Federal Deposit Insurance Corp.-assisted deal that extended its reach in Illinois and Wisconsin. It also said earlier this month when it reported fiscal fourth-quarter results that it would continue making small “tuck-in” acquisitions to build its business.

Bank of Montreal is Canada’s fourth-largest lender. It expects the M&I acquisition to be accretive to earnings in 2013, excluding one-time merger and integration costs of about C$540 million. \