The North Carolina-based bank had launched its case after its agreement to acquire the Dutch Bank's US unit La Salle appeared to have been stymied by a court ruling from Dutch regulatory authorities on May 4th.
However, a subsequent ruling overruled the initial decision that the deal required shareholder approval, and cleared the way for the $21 billion acquisition to go ahead.
The deal will now require approval from the Federal Reserve Board.
Christopher Feeney, spokesman for BofA, said that the decision to abandon proceedings was taken because "there is no longer any legal impediment to close the LaSalle transaction".
Should the deal go through, it boost BofA's branch network by 411 outlets to 6,100.
The fate of LaSalle has figured prominently in the ongoing wrangle between a Royal Bank of Scotland-led consortium and Barclays Bank to acquire ABN Amro.
Prior to the most recent court ruling that cleared the way for Bank of America's acquisition, the consortium's offer had been conditional on the inclusion of LaSalle.