His testimony before the House oversight and reform committee on 7 February will be the first major public oversight hearing for Democrats, who have promised greater scrutiny of Trump after winning control of the House in the 2018 midterm elections.
Cohen, who served as Trump's attorney and fixer for years, came under scrutiny from federal prosecutors in NY over hush money payments he orchestrated during the 2016 presidential campaign to silence Stormy Daniels and Karen McDougal, two women who alleged having extramarital affairs with Trump.
Trump's attorney Rudy Giuliani described Cohen to Fox News as "a thoroughly discredited liar", and said he could not imagine why Cummings would want to hear from Cohen.
Cohen said Trump directed him to make the payments because of concern about how they might affect the election campaign, adding that, "nothing at the Trump Organization was ever done unless it was run through Mr. Trump".
"I thank Michael Cohen for agreeing to testify before the Oversight Committee voluntarily", said Oversight Chairman Elijah Cummings, a Democrat from Maryland, in a statement.
On Thursday, Cohen said in a statement that he had accepted Cummings' invitation to testify "in furtherance of my commitment to cooperate and provide the American people with answers". Cummings is also requesting a raft of potentially revealing communications about the payments and other legal services Cohen provided for the president and his company.
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Trump was directly implicated by Cohen's campaign finance guilty plea, as Cohen and prosecutors have told the court that the payments were made in coordination with the then-candidate.
The women have claimed they had affairs with Trump after the real estate mogul married his third wife, Melania.
As Trump's longtime lawyer and "fixer", Cohen had connections to a number of the key questions surrounding the president, the Mueller probe and now the Democratic congressional investigations.
On the issue of possible collusion between the Trump campaign and Russia, Giuliani says, "Cohen doesn't know a damn thing about collusion".
The House Intelligence Committee has been seeking a closed-door session with Cohen to discuss Russia-related matters. Cohen also acknowledged in the Mueller investigation that he lied to Congress by saying negotiations over a Trump Tower in Moscow had ended in January 2016 when he actually pursued the project into that June, well into Trump's 2016 presidential campaign.
Cohen has testified behind close doors to both the Senate and the House previously, some of which led to his conviction on lying to Congress. House Intelligence Committee Chairman Adam Schiff, D-Calif., said he welcomes Cohen's testimony before the oversight panel, but "it will be necessary, however, for Mr. Cohen to answer questions pertaining to the Russian Federation investigation, and we hope to schedule a closed session before our committee in the near future".
The president has assailed the various investigations, while Russian Federation has denied trying to interfere in the 2016 election for the purposes of sowing discord and improving Trump's prospects.