Cohen's appearance in public, before national television cameras, will begin to fulfill that promise, but is likely to only be the first of a string of public testimony that could prove damaging to the president.
They now hold the chairmanship of committees with the power to hold hearings, inviting or forcing witnesses to testify in public.
That means that he wants to talk.
Cohen said he will "give a full and credible account of the events that have transpired".
Cohen, 52, also pleaded guilty to eight separate counts, including campaign finance violations, that he said were carried out at the direction of Trump.
Known as Trump's "fixer", part of Cohen's job was to make the president's problems go away - by any means necessary.More news: 5 women to watch at the Australian Open
He did make a brief statement in court in which he said he "was weak for not having the strength to question and to refuse his demands".
After more than a decade as Trump's personal lawyer, Cohen has plenty of dirt on the president.
In the interview with Stephanopoulos, however, Cohen rejected Trump's claims as "absolutely not true".
It's unclear whether Cohen's testimony contains evidence that could lead to the impeachment of the U.S. president, but given the fact that Trump's casually-tweeted comments (such as criticisms of the Federal Reserve chairman Jerome Powell) have been correlated with major turbulence in the stock markets, the last thing the economy needs at the moment is another wild card.
Michael Cohen wil testify to Congress on February 7.
Cummings said the committee has no intention of interfering in ongoing criminal probes.More news: Former Miss SA Demi-Leigh engaged to American sport star Tim Tebow
"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.
"Cohen has agreed to testify publicly before the House Oversight Committee, cooperating with Robert Mueller over crimes that he says were directed by Donald Trump", Tapper said. He said, "To that end, we are in the process of consulting with Special Counsel Mueller's office".
A federal judge in Manhattan sentenced him to three years in federal prison.
Cohen, in a statement, said he agreed to testify in "furtherance of my commitment to cooperate and provide the American people with answers". Trump has denied the trysts. The investigation has clouded Trump's presidency.
Since then, Cohen has spent more than 70 hours with federal prosecutors in Manhattan as well as with Mueller, who is investigating Russian efforts to influence the 2016 election and Trump's campaign.
House Intelligence Committee Chairman Adam Schiff, a California Democrat who had been seeking to bring Cohen before his committee, issued a statement on Thursday saying he hopes to schedule his own session with Cohen behind closed doors.More news: Ryder Cup captain Harrington putting 'legacy' on line