WASHINGTON—President Trump said Friday he would nominate former campaign adviser Stephen Moore to serve on the Federal Reserve’s board of governors, which would place a fierce critic of the central bank’s leadership inside the consensus-oriented institution.

Mr. Trump made the offer to Mr. Moore earlier this past week, an administration official said, after reading an opinion article Mr. Moore and a co-author wrote criticizing Fed Chairman Jerome Powell, a regular target of Mr. Trump’s disapproval. The article was published last week in The Wall Street Journal, where Mr. Moore previously worked as an editorial-page writer.

“I have known Steve for a long time and have no doubt he will be an outstanding choice,” Mr. Trump said on Twitter Friday. In a brief telephone interview before Mr. Trump’s announcement, Mr. Moore said he would be eager to serve in the position.

Mr. Moore hasn’t gone through the customary vetting process that is typical before a presidential announcement, the official said, which means it could take weeks or months before the nomination is formally submitted for Senate confirmation.

The Fed’s seven-member board has two vacancies.