The lawyer has cooperated with Mueller's investigation into Russian interference in the election since past year, which has prompted anger from the president.
Former U.S. federal prosecutor Roland Riopelle called it "a very frightening development" for Trump.
Cohen is expected to face tough questions about hush-money payments he arranged on Trump's behalf to keep extramarital affair allegations out of the news during the 2016 presidential election.
"I look forward to assisting Michael to state publicly all he knows about Mr. Trump - and that includes any appropriate congressional committee interested in the search for truth and the difference between facts and lies", Davis said in a statement at the time. "And much of it has been blacked out in the court documents, so far". In New York, he acknowledged his involvement in payments to porn actress Stormy Daniels and former Playboy model Karen McDougal.
The women have claimed they had affairs with Trump after the real estate mogul married his third wife, Melania.
The president said he did nothing wrong in the campaign finance charge, and he accused his former lawyer of lying to prosecutors to try to get a reduced sentence.
When asked by a reporter about Cohen's upcoming testimony during his visit to the southern border on Thursday, Trump said he isn't concerned.
Trump and his backers also tried to downplay the payments, calling them a "simple private transaction", even though they could run foul of campaign finance laws.
The Democrats promised to use their new majority in the House of Representatives to delve deeper than ever before into Donald Trump's pre-presidential background. He is set to testify before the House Oversight and Reform Committee, which is investigating payments made during the 2016 campaign to silence women who claimed to have had sex with Trump.
Cohen also lied about whether he and Trump, referred to as "Individual 1" in the November court documents, discussed planning a trip to Russian Federation during the campaign.
In a statement, Chairman Elijah Cummings, who invited Cohen to testify, said his committee will avoid "inappropriately interfering with any ongoing criminal investigations". "The Committee will announce additional information in the coming weeks".
Cummings has signalled that his committee is more interested in investigating the president's involvement in the campaign violations to which Cohen pleaded guilty previous year.
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.
One issue is Trump Tower Moscow. But the voters weren't fully aware of its existence.
In a statement, Cohen said he made the decision to testify voluntarily before Congress in furtherance of his effort to "commitment to cooperate and provide the American people with answers".
Trump has lashed out at Cohen over his cooperation with prosecutors, recently saying Cohen "lied" and deserved to "serve a full and complete sentence".