Press secretary Sarah Sanders said the president extended the offer directly to Kudlow and that he has accepted the role.
“Larry Kudlow was offered, and accepted, the position of Assistant to the President for Economic Policy and Director of the National Economic Council. We will work to have an orderly transition and will keep everyone posted on the timing of him officially assuming the role,” Sanders said in a statement.
Kudlow will replace Gary Cohn, who resigned last week as the president's chief economic adviser after he lost his fight to stop Trump from imposing steep tariffs on steel and aluminum imports.
Kudlow, a CNBC commentator, also has previously opposed tariffs, but Trump said Tuesday that Kudlow has "come around" on the issue.
The president has made no secret about Kudlow being a top contender for the job, noting his early support for his presidential bid even as he acknowledged, and welcomed, their philosophical disagreements on some economic issues.
"I've known him a long time. We don't agree on everything. In this case, I think it's good. I want a diverging opinion," Trump said Tuesday.