WASHINGTON—The Labor Department sent its proposed overtime rule to the White House for review, which could allow the regulation determining how many Americans are entitled to extra pay when working more than 40 hours to be finished by late this year.

The department has sent the rule to the Office of Information and Regulatory Affairs, an arm of the White House’s Office of Management and Budget, two administration officials said. That is typically a sign the regulation is close to a public unveiling.

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