Mr. Kudlow has long espoused a traditional conservative embrace of free trade, but it remains to be seen how vocally he will push back on the growing ascendance of West Wing advisers who are trade skeptics and have urged Mr. Trump to adopt protectionist measures to protect American industry.

Stock markets, which have been rattled by the White House tariffs, did not react positively to news of Mr. Kudlow’s appointment on Wednesday. The Dow Jones industrial average was down more than 200 points for most of the afternoon, once news media outlets began reporting Mr. Kudlow was the pick.

Mr. Kudlow is a radio and television commentator and an economics consultant. He was a zealous convert to the supply-side economic policies that swept the Republican Party in the late 1970s. He is a protégé of the supply-side economist Arthur Laffer, with whom Mr. Kudlow worked on Ronald Reagan’s 1980 presidential campaign. Mr. Kudlow went on to serve in Mr. Reagan’s Office of Management and Budget.

Like many past National Economic Council directors, he is not an academically trained economist — he studied for a master’s degree at Princeton University but did not earn one — but he served as chief economist for Bear Stearns and made a name advising prominent conservative politicians. In the early 1990s, Mr. Kudlow took a leave from the firm to enter treatment for drug and alcohol addiction; his colleagues said he abused cocaine.

Mr. Kudlow has spoken frequently about his addiction and ensuing sobriety in the ensuing years.

He said Thursday that staying clean and sober for nearly 23 years “is the center of my life” and “my No. 1 job.”

Asked whether he thought the substance abuse could prove problematic for him as a White House staff nominee, he said, “We’ll see how that plays out.”

Mr. Kudlow was an early and enthusiastic supporter of Mr. Trump’s run for the presidency, advising the neophyte candidate on economic issues and pushing him to go big on cutting taxes. The men agreed on their desire for growth-goosing tax cuts but disagreed on trade, on which Mr. Trump ran as a populist and Mr. Kudlow preached free-market principles.