In a statement to CNN, Cohen said on Thursday that he has agreed to testify before the House Oversight Committee "in furtherance of my commitment to cooperate and provide the American people with answers".
"I look forward to having the privilege of being afforded a platform with which to give a full and credible account of the events which have transpired," Cohen said.
Cohen is likely to face questions about the June 2016 Trump Tower meeting between senior members of President Donald Trump's campaign and a Russian lawyer as well.
Thursday's announcement comes after Cohen pleaded guilty and was sentenced in December to three years in prison on multiple charges, including two campaign finance crimes tied to illicit payments made to silence women during the presidential campaign.
Cohen cooperated with Special Counsel Robert Mueller's investigation after his August guilty plea.
Mueller's team in court filings wrote that Cohen provided "useful information concerning certain discrete Russia-related matters core to its investigation".
House Oversight Committee Chairman Elijah Cummings said that Mueller cleared Cohen's testimony before it was agreed to, CNN said.
"He'll have a chance to tell his side of the story, and we'll have a chance to question him. The American people deserve that," Cummings said.
"We don't want to do anything to interfere with the Mueller investigation."
Other members of the Trump administration are likely to be summoned to Capitol Hill also.
House Judiciary Chairman Jerry Nadler of New York is demanding acting Attorney General Matt Whitaker testify this month, and he's threatening a subpoena if Whitaker won't voluntarily appear.