A new financial disclosure from President Donald Trump acknowledged that he reimbursed his lawyer, Michael Cohen, for a $130,000 payment to an adult-film star just before the 2016 election, the first time the president has officially stated the payment in government disclosures.

A footnote in Mr. Trump’s 2017 financial disclosure released Wednesday documented a reimbursement of between $100,001 and $250,000 for expenses in 2016 to his attorney for payment to Stephanie Clifford, known professionally as Stormy Daniels. The...