President-elect Donald Trump is expected to select Wilbur Ross Jr. to head the Commerce Department, said two people familiar with the deliberations, a decision that would put a billionaire investor known for buying up failed companies in charge of the agency tasked with cultivating economic growth.

Mr. Ross, 78 years old, is chairman and chief strategist of private-equity firm W.L. Ross & Co., a company known for deals that included combining bankrupt steel producers Bethlehem Steel, Acme Steel, Weirton Steel and LTV Steel...