Cohen is a pivotal figure in the investigation by special counsel Robert Mueller into potential coordination between Russian Federation and the Trump campaign.
That doesn't mean Cohen's testimony won't have dramatic reveals.
He's claimed the president directed him to arrange the hush money payments.
Trump has denied having the extramarital affairs.
"Last November, the American people voted overwhelmingly for Congress to do two things - address the core issues that affect their daily lives, and fulfill our Constitutional responsibility to serve as an independent check and balance on the executive branch by restoring accountability and transparency", Mr Cummings said in a statement.
The session will come just under a month before he is due to turn himself in for a three-year prison sentence.
Cohen has directly implicated Trump in a series of campaign finance violations in 2016, saying that the then-Republican nominee for president, known in court documents as "Individual 1" told him to pay hundreds of thousands of dollars to two women, Stormy Daniels and Karen McDougal, to keep them quiet about affairs he had with them in the 2000s.
Says Joe, a New Jersey resident: "I think he (Trump) is going to resign". He said he accepted the invitation "in furtherance of my commitment to cooperate and provide the American people with answers". Cohen spoke in 2017 to the House and Senate Intelligence Committees - and later pleaded guilty to lying to Congress about the Trump Tower Moscow timeline - and both Schiff and Senate Intelligence Chairman Richard Burr say they want to speak to him again before he begins his jail sentence in March.
"It's my understanding that he doesn't intend to address the Russian Federation investigation in his open testimony. At the end of the day, there are questions he needs to answer".
It was unclear if Cohen's agreement to testify before the Oversight Committee will preclude appearances, in public or private, before other House panels. Cohen will testify publicly before Congress in February 2019.
The committee's chairman, Rep. "I want to be clear on that".
Cohen's hearing date is subject to change, Cummings noted. Cummings has asked for that information to be returned by January 22.
"I hope you will work with me and the minority members to avoid an unproductive and chaotic hearing", Jordan wrote. They focused instead on what they asserted was anti-Trump bias in the Justice Department and the Federal Bureau of Investigation.
"Mr. Cohen has expressed an interest in telling his personal story in open session, and we welcome his testimony before the Committee on Oversight and Reform", he said.
Rep. Mark Meadows, R-N.C., who sits on the oversight panel, accused Democrats Thursday of making "a political decision, not an oversight decision" in calling Cohen to testify.
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