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.”

Some Republican lawmakers attacked Mr. Cohen ahead of Wednesday’s hearing. Rep. Matt Gaetz (R., Fla.) tweeted Tuesday at Mr. Cohen: “Do your wife & father-in-law know about your girlfriends? Maybe tonight would be a good time to chat.”

Lanny Davis, a lawyer for Mr. Cohen, called the tweet a “new low.”

Mr. Cohen’s testimony on Wednesday is expected to focus on his “behind-the-scenes” accounts of working for Mr. Trump for over a decade, a period during which Mr. Cohen plans to say he witnessed “lies, racism and cheating” by Mr. Trump, the person said.

Mr. Cohen is expected to recount racist remarks Mr. Trump allegedly made to him, including instances in which Mr. Trump allegedly questioned the intelligence of African-Americans and criticized their lifestyle choices, the person said.

Mr. Cohen’s planned testimony comes 13 months after the Journal first reported that Mr. Cohen paid $130,000 in October 2016 to former adult-film star Stephanie Clifford, known as Stormy Daniels, to buy her silence after she alleged having a sexual encounter with Mr. Trump.

Michael Cohen, President Trump’s former personal attorney, was sentenced to three years in prison. In court, he said his blind loyalty to President Trump led him ‘to take a path of darkness.’ (Photo: Timothy A. Clary/AFP/Getty Images)

In his testimony Wednesday, Mr. Cohen will provide documentation of his reimbursement for the $130,000 Clifford payment, which he received in monthly installments of $35,000 throughout 2017, the person familiar with his testimony said. Mr. Cohen intends to show the panel a signed check, the person said.

Mr. Trump signed some of the checks reimbursing Mr. Cohen, which Mr. Cohen began receiving after Mr. Trump took office, according to another person familiar with the payments.

The payments to Mr. Cohen were characterized by Trump Organization Chief Financial Officer Allen Weisselberg as legal fees, but federal prosecutors have said the monthly invoices weren’t in connection with any legal services Mr. Cohen provided at that time.

After the 2016 election, Mr. Weisselberg authorized a payment of double what Mr. Cohen had paid Ms. Clifford to cover related income taxes, as well as adding a $60,000 bonus, the Journal has previously reported.

In the wake of the Journal’s revelations, federal prosecutors investigated Mr. Cohen’s activities, raided his home, hotel room and office, and began probing the business practices of the Trump Organization, including whether it committed campaign-finance violations. The Trump Organization investigation, spearheaded by the U.S. attorney’s office in Manhattan, is continuing, people familiar with the matter said.

White House press secretary Sarah Sanders in a statement called Mr. Cohen a “disgraced felon” and noted that he had previously pleaded guilty to lying to Congress and making other false statements.

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“Sadly, he will go before Congress this week and we can expect more of the same,” she said. “It’s laughable that anyone would take a convicted liar like Cohen at his word, and pathetic to see him given yet another opportunity to spread his lies.”

A spokesman for the Trump Organization didn’t respond to a request for comment.

Mr. Cohen agreed to testify before the committee at the behest of its Democratic chairman, Rep. Elijah Cummings of Maryland, after postponing his scheduled hearing last month, citing public statements by Mr. Trump he saw as threats toward members of his family.

In August Mr. Cohen implicated the Republican president in two federal crimes when he told prosecutors Mr. Trump directed hush-money payments during the 2016 campaign to Ms. Clifford and to former Playboy model Karen McDougal, who alleged she had an affair with Mr. Trump.

The person familiar with Mr. Cohen’s anticipated testimony said Mr. Cohen would provide “evidence of criminal conduct since Mr. Trump became president,” but other than saying it involved the Clifford payment, wouldn’t offer more specifics before Wednesday’s House hearing.

The hearing would be the first time Mr. Cohen alleges that Mr. Trump committed a crime while in office. While the payments to both women were made in the weeks before the 2016 presidential election, Mr. Trump has faced questions from reporters about his possible knowledge of Mr. Cohen’s subsequent reimbursement for the Clifford payment, as well as about whether he discussed with Mr. Cohen efforts to conceal the payment after the Journal first reported its existence in January 2018.

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The president has denied the sexual encounters with the women as well as ordering Mr. Cohen to arrange the payments to them.

In December, federal prosecutors in New York for the first time directly implicated the president in the payoff scheme, referring to him in court papers as “Individual-1,” alleging that Mr. Trump had played a key role in the hush payments, as the Journal had previously detailed in its reporting.

Mr. Cohen pleaded guilty to eight federal crimes in August, including tax evasion and making false statements to a bank, and to one count of lying to Congress in November. He is expected on Wednesday to express contrition about the crimes he committed and acknowledge his mistakes, the person said. He will attest to having lied repeatedly to protect Mr. Trump and to what led him to publicly break with the president last summer, the person said. He will also reiterate that he wouldn’t accept a presidential pardon from Mr. Trump if one were offered, the person said. Mr. Cohen is scheduled to begin a three-year prison term on May 6.

Mr. Cohen plans to give his most detailed public account to date of Mr. Trump’s alleged direction of the hush payments, as well as how Mr. Trump was involved in efforts to conceal them from the public weeks before the 2016 election, according to the person.

He also plans to allege that Mr. Weisselberg, the Trump Organization’s chief financial officer, was involved in those efforts, the person said.

The Journal first detailed Mr. Cohen’s account to prosecutors of Mr. Weisselberg’s involvement in November. Mr. Weisselberg was granted immunity by federal prosecutors in the investigation and testified before a grand jury, according to a people familiar with the matter.

A lawyer for Mr. Weisselberg declined to comment.

Mr. Cohen spent more than a decade working for Mr. Trump, first at the Trump Organization and later as his personal lawyer. But the pair had an often turbulent relationship: Mr. Trump at one point asked senior aides to persuade Mr. Cohen to resign, and later slashed his annual income of more than $400,000 roughly in half, the Journal has previously reported.

Meanwhile, Mr. Cohen for more than a decade remained unswervingly loyal, and ultimately found a niche as a fixer of some of Mr. Trump’s thornier problems. In 2017, Mr. Cohen told Vanity Fair: “I’m the guy who would take a bullet for the president.” Less than a year later, Mr. Cohen publicly broke with the president, saying he was putting his family and country first.

In a memo released last week, Mr. Cummings said that in addition to the hush-money payments, Mr. Cohen’s testimony would focus on the president’s compliance with tax laws, his “potential and actual conflicts of interest,” his business practices and “the accuracy of the President’s public statements,” among other matters.

Mr. Cohen won’t answer questions related to special counsel Robert Mueller’s investigation into whether Mr. Trump or any of his associates colluded with Russia to interfere in the 2016 U.S. election, according to a person close to Mr. Cohen. Mr. Trump has denied collusion, as has Russia.

Mr. Cohen is expected to explain why he lied to Congress in 2017 to play down Mr. Trump’s involvement in efforts during the campaign to build a Trump Tower in Moscow but isn’t expected to say whether Mr. Trump had directed him to make those misstatements, according to the person familiar with Wednesday’s planned testimony. Mr. Cohen will tell the committee that Mr. Trump continued to inquire about the project months past January 2016—the month Mr. Cohen cited before Congress in 2017 as when the project ended, this person said.

Mr. Cohen is set to speak before the House Intelligence Committee on Thursday.

Republicans on the Oversight Committee plan to try to undercut and discredit Mr. Cohen’s testimony by raising questions about his motivations for speaking to Congress.

Republicans plan to ask Mr. Cohen the reason for the “sudden righteousness” that led him to plead guilty and implicate the president in crimes, according to a GOP lawmaker on the committee. They also plan to ask who is paying his legal fees; why he fired his former attorney, Guy Petrillo; and to whom he has spoken about his conversations with investigators, the lawmaker said.

In a letter last week to the chairman, GOP Reps. Jim Jordan of Ohio and Mark Meadows of North Carolina accused the panel under Mr. Cummings’s leadership of being “out to attack the president for partisan gain,” noting that Mr. Cohen had previously lied to Congress in a 2017 hearing. They said they intended to question Mr. Cohen about his “conduct throughout his professional life and any other financial dealings he has had, including with his father-in-law.”

The documents Mr. Cohen plans to discuss in his public testimony partly reflect a way for Mr. Cohen to deflect attacks from Republican members of the committee, the person familiar with his plans said, adding: “He expects to be called a liar.”

—Nicole Hong and Michael Rothfeld contributed to this article.

Write to Rebecca Ballhaus at Rebecca.Ballhaus@wsj.com and Warren P. Strobel at Warren.Strobel@wsj.com