Under the deal, FleetBoston investors will receive stock worth $45 for each of their shares, representing a 40% premium over the bank's closing price last Friday.
The transaction is believed to be the biggest acquisition since the $59bn tie-up between pharmaceutical giants Pfizer and Pharmacia in July last year.
The combined company will displace JP Morgan as the second-biggest bank in the US, behind sector leader Citigroup.
Bank of America is currently ranked number three, with FleetBoston in seventh position.
Consumer giant
But the two firms said their tie-up would create the biggest consumer bank in the US, serving about 33 million personal account holders as well as 2.5 million business customers.
Bank of America boss Kenneth Lewis will become chief executive of the combined bank, while FleetBoston's Charles Gifford will take on the role of chairman.
"This merger is about delivering the combined capabilities of two powerful organisations to our customers, shareholders and communities," Mr Lewis said in a statement.
The two companies said they aimed to complete the merger by the middle of next year.
According to US media reports, FleetBoston's outlets in the north-east of the country will be rebranded under the Bank of America name.