Jim R. Bounds/Bloomberg

The PNC Financial Services Group announced on Monday that it had signed an agreement to buy the American retail business of the Royal Bank of Canada for $3.45 billion.

The deal, which is priced at a $112 million discount to tangible book value, will allow PNC to expand into the Southeast. The R.B.C. unit has 424 branches in North Carolina, Florida, Alabama, Georgia, Virginia and South Carolina, and roughly $25 billion of assets.

Once the acquisition of the RBC Bank subsidiary is complete, PNC will have the fifth-largest number of bank branches in the United States. PNC anticipates that the deal will increase earnings by 2013.

“The addition of RBC Bank provides PNC a great opportunity to enter attractive Southeast markets in a way that will create value for our shareholders,” James E. Rohr, chief executive of PNC, said in a statement. “This transaction represents an outstanding growth opportunity for PNC.”

With the divestiture, Royal Bank of Canada is selling a business that has struggled as a result of the housing crisis. The Canadian bank acquired the unit, then named Centura Banks, for $2.2 billion in 2001. But the group has struggled to gain market share, even after a number of transactions.

Royal Bank of Canada is among several Canadian banks that looked to the United States for growth with varying degrees of success. The BMO Financial Group, the parent of Bank of Montreal, agreed in December to buy Marshall Ilsley, a bank based in Milwaukee, for $4.1 billion. The TD Bank Financial Group, based in Toronto, bought Commerce Bancorp of New Jersey for $8.6 billion in 2008, and last year bought three failed banks in Florida.

Bank of America Merrill Lynch and the law firm Wachtell, Lipton, Rosen Katz advised PNC. RBC Capital Markets, JPMorgan Chase and Sullivan Cromwell worked with Royal Bank of Canada.

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