(CNN) President Donald Trump's former lawyer Michael Cohen will testify before the House Oversight Committee, the first major move by House Democrats to haul in a member of Trump's team connected to special counsel Robert Mueller's investigation, according to a schedule published by the committee.

Cohen has agreed to testify publicly before the panel on February 7, according to a statement from Cohen.

Cohen is coming to Capitol Hill after he 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 — crimes that prosecutors say Trump directed Cohen to commit.

Cohen cooperated with Mueller's investigation after his August guilty plea, and his congressional testimony could thrust some of those still-private details he provided into the public sphere. Mueller's team in court filings wrote that Cohen provided "useful information concerning certain discrete Russia-related matters core to its investigation."

In a statement to CNN, Cohen said he agreed to testify "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.

House Oversight Committee Chairman Elijah Cummings, a Maryland Democrat, said that Mueller cleared Cohen's testimony before it was agreed to.

"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."

There may be some topics at the hearing that are off limits. House Intelligence Chairman Adam Schiff, who has also been seeking testimony from Cohen, told CNN that Cohen's lawyers indicated Cohen could not discuss the Russia investigation publicly, and his panel wants Cohen to testify behind closed doors.

"He is going to need to answer questions about it," Schiff said. "He hasn't agreed but I think there's a good likelihood. ... At the end of the day, there are questions he needs to answer."

Cohen's cooperation with Mueller prompted a falling out with his former client, with Trump attacking Cohen on Twitter, including accusing him of lying to try to lessen his jail sentence. Trump has denied directing Cohen to pay women who alleged affairs with Trump.

Cohen addressed his relationship with Trump at his sentencing, saying he had "blind loyalty to this man that led me to choose a path of darkness over light."

"Recently, the President tweeted a statement calling me 'weak,' and he was correct, but for a much different reason than he was implying," Cohen said at the time. "It was because time and time again I felt it was my duty to cover up his dirty deeds rather than to listen to my own inner voice and my moral compass."

Republicans may point to Cohen's credibility problems, given he pleaded guilty to lying to Congress.

"I think that his trustworthiness is somewhat suspect by even those who love what he says," said Rep. Mark Meadows, a North Carolina Republican.

Ohio Rep. Jim Jordan, the top Republican on the Oversight Committee, said that the Cohen hearing suggested that Cummings "will be using the committee as a venue for political theater rather than legitimate oversight."

"The Democrats' star witness has admitted to providing intentionally false and misleading testimony to Congress. He is also a witness in ongoing law-enforcement matters, including Special Counsel Mueller's probe," Jordan said in a statement. "When in the minority, Chairman Cummings and the Democrats have often cautioned against such actions. Now that Chairman Cummings is in charge, the same standards don't seem to apply. This makes clear that Chairman Cummings and the Democrats will do whatever it takes to attack this President."

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.

One issue is Trump Tower Moscow. Cohen worked on the Moscow project during the 2016 presidential campaign, which included outreach to Russian officials. Cohen initially lied and said the Trump Tower Moscow talks ended in January 2016, but he admitted last month those conversations extended through June 2016 when he pleaded guilty to lying to Congress about the project.

Mueller's court filings revealed that Cohen had spoken to a Russian in 2015 who had offered "political synergy" with the Trump campaign while discussing Trump Tower Moscow.

The payments made or orchestrated to women during the campaign -- to adult-film star Stormy Daniels and former Playboy model Karen McDougal -- to stay silent about alleged sexual encounters with Trump are also sure to be a hot topic at the congressional hearing.

Cohen is likely to face questions about the June 2016 Trump Tower meeting between senior members of the Trump campaign and a Russian lawyer as well.

The announcement of Cohen's testimony is the latest sign that House Democrats plan to make oversight of every aspect of Trump's life a key part of their control of the House.

It's not yet clear whether Cohen will agree to speak to any other committees. 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.

"Mr. Cohen has had in his possession for months a request to return to the Senate Intelligence Committee for additional closed-door testimony, made all the more necessary by Mr. Cohen's indictment and guilty plea for making false statements to Committee investigators," Burr said in a statement. "The request still stands, regardless of any public testimony Mr. Cohen may give on other issues."

Others in Trump's personal orbit are also facing scrutiny, and House Democrats, having retaken the majority earlier this month, now have subpoena power. On the House Intelligence Committee, Schiff has said he will issue a subpoena if necessary to obtain Donald Trump Jr.'s phone records to find out who Trump's son called when Trump Jr. called a number blocked in phone records while setting up the June 2016 Trump Tower meeting.

Trump's administration officials are likely to be summoned to Capitol Hill, too. 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.

This story has been updated with additional developments Thursday.