Billionaire financier Howard Lutnick, President Donald Trump’s choice to lead the Commerce Department, said Wednesday that he would sell all of his business holdings within 90 days.

WASHINGTON—Howard Lutnick’s journey from Wall Street veteran to one of President Trump’s most hawkish trade advisers began with a speech at an October campaign rally at Madison Square Garden. Lutnick extolled the virtues of tariffs and argued that the duties could at least in part replace the U.