Payment will be made using $26.2 billion in excess assets and $18.8 billion from the sale of securities.
The organization said it was settling its debts to avoid spending billions in interest on its repayments.
It has already handed over more than $2.5 billion in dividends to the US Treasury and has estimated that it will save $3.6 billion a year by paying everything back now.
The move is a coup for outgoing chief executive and president Kenneth Lewis, who is set to leave Bank of America at the end of the year.
"We believe that this is good news, not only for the US taxpayer and our company, but for the country as it is a milestone indicating that public policy has succeeded in helping our industry and the economy begin to recover," he said.
The TARP repayment is the latest in a series of moves by Bank of America in its attempt to free itself of government control.
It has already paid the government $425 million to terminate an asset guarantee sheet, as well as opting out of the Temporary Liquidity Guarantee Program three months ago.
US pay czar Kenneth Feinberg has expressed his delight with the news of the TARP repayment, telling Reuters that it was "very satisfying" and "exactly the goal" of his oversight programme.
Much of the deal was believed to have been negotiated by the firm's chief risk officer Gregory Curl.
He is believed to be one of the leading contenders to take Mr Lewis' chair when he retires and financial industry insiders have speculated that his work on the repayment scheme has boosted his chances of ascending to Bank of America's top job.
Last month, as part of its drive to rebuild its public image, Bank of America announced it will be handing $20 million over to non-profit neighbourhood organizations in the US and the UK.
By Tony Aynsley