Mnuchin, who was Trump's presidential campaign finance chairman, could be named as early as Wednesday, said a Republican source close to the decision.
Mnuchin was chosen over several high-profile candidates, including JPMorgan Chase Chairman Jamie Dimon and Republican US Representative Jeb Hensarling, chairman of the powerful House Financial Services Committee.
Mnuchin is the first person with extensive Wall Street experience to head the Treasury since his former boss, Henry Paulson, the former Goldman Sachs chief executive who served under President George W. Bush and steered Treasury through the chaotic initial stages of the 2008-2009 financial crisis.