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Kudlow previously worked for the White House during President Ronald Reagan's administration. He acted as an informal advisor to Trump during the campaign.
Kudlow confirmed to CNBC on Wednesday that he had accepted the job. Like Cohn, Kudlow is a proponent of free trade. He previously called Trump's tariffs on steel and aluminum a "bad omen."
Trump may also get a chance to comment on Tuesday's special election in Pennsylvania. Democrat Conor Lamb appears to have beaten Republican Rick Saccone in a razor-thin race for the House district, wiping out the 20-point Republican spread Trump received during the 2016 election.