Michael Cohen, Donald Trump’s former lawyer, plans on Wednesday for the first time to publicly accuse the president of engaging—while in office—in criminal conduct related to a hush-money payment to a porn star, a person familiar with his expected testimony before Congress said.

Appearing before the House Oversight Committee, Mr. Cohen also plans to make public some of Mr. Trump’s private financial statements and allege that Mr. Trump at times inflated or deflated his net worth for business and personal purposes, including avoiding paying property taxes, the person said. The financial statements were developed by Mr. Trump’s accountant, the person said. The Wall Street Journal hasn’t seen those statements.

On Tuesday morning, Mr. Cohen met behind closed doors with the Senate Intelligence Committee. Upon leaving the hearing after nearly nine hours, he said he appreciated the opportunity to “clear the record and to tell the truth,” adding he looked forward to telling his story “in my voice” on Wednesday.

“I’m going to let the American people decide exactly who’s telling the truth,” he said.

Referring to Tuesday’s closed-door testimony, Sen. Roy Blunt (R., Mo.), said, “I’d say the tone was serious.”