Boston ? Bank of America Corp. announced an agreement Monday to buy FleetBoston Financial Corp., a deal initially valued at $47 billion that would swallow up the last of the big Boston banks that made the city a financial center.

The agreement, if approved by shareholders and regulators, would create the nation’s second-biggest banking company. Bank of America, currently No. 3, would have about 33 million customers and 2.5 million business clients in 35 countries.

The deal also would bring Bank of America into New England and eliminate the Fleet name.

“We are now truly the bank of America,” said Kenneth Lewis, chairman and chief executive of Bank of America.

FleetBoston chairman and CEO Charles Gifford said there would be some layoffs. FleetBoston has 47,700 employees; Bank of America has 133,000.

Gifford said he did not know how the deal would affect the Fleet Center, where the Boston Celtics and Bruins play. The Fleet name is everywhere in New England, from the arena to a waterfront concert pavilion.

“I’d love for it to be the Bank of America Center,” Lewis said Monday.

The merger combines banks with assets totaling more than $930 billion.

In trading Monday on the New York Stock Exchange, FleetBoston shares climbed to $39.20, while Bank of America shares fell to $73.57, down $8.29, or 10 percent. That reduced the value of the offer to $42.9 billion.

Kenneth Lewis, left, Bank of America chairman and CEO, and FleetBoston Financial Corp. chairman and CEO Charles Gifford listen to questions during a press conference in New York. They announced the merger of the two banks on Monday.