WASHINGTON—The White House has notified Federal Reserve governor Jerome Powell that President Donald Trump intends to nominate him as the next chairman of the central bank, according to a person familiar with the matter, a move likely to combine continuity on interest-rate policy with perhaps a lighter touch on financial regulation.

If confirmed by the Senate, Mr. Powell would succeed Fed Chairwoman Janet Yellen, the central bank’s first female leader, whose four-year term as Fed chief expires in early February.

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