Cohen acknowledged the testimony in a separate statement: "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".
It promises to be a contentious hearing.
Cohen has pleaded guilty in both investigations and was sentenced last month to three years in prison.
Former U.S. federal prosecutor Roland Riopelle called it "a very frightening development" for Trump.
He admitted he had paid hush money to two women who could have embarrassed Mr Trump with details of their alleged affairs with him. "And much of it has been blacked out in the court documents, so far".
Adult film star Stormy Daniels, whose legal name is Stephanie Clifford, was paid $130,000 and former Playboy model Karen McDougal was paid $150,000 by Cohen.
The women have claimed they had affairs with Trump after the real estate mogul married his third wife, Melania.
After Cohen reached a plea deal, Trump criticized him for being "a weak person".
Cohen, in an interview with ABC News in December, scoffed at that assertion.
Cohen has a track record of erratic and unethical behavior, caught on tape at one point threatening a Daily Beast reporter with complete financial and social ruin if he published a story with the words "Trump" and "rape" regarding an accusation made by Trump's first wife.
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.
A judge also ordered Cohen to forfeit $692,000 and pay restitution of almost $1.9 million.
Cummings said the committee was "in the process of consulting with Special Counsel [Robert] Mueller's office" to ensure that Cohen's scheduled testimony would not interfere with the ongoing investigation into interactions between the Trump campaign and Russian officials. "The Committee will announce additional information in the coming weeks". This hearing will place the president's alleged crimes and extensive shady dealings - as well as the Russian Federation investigation - at the center of political life in Washington D.C. with potentially major repercussions for the country. But there are probably many other aspects of his ten years with Donald Trump that will come into focus, whether it's the Moscow hotel or the other various hotels in which Donald Trump invests in Toronto and Soho and in Panama. But the voters weren't fully aware of its existence.
He said he accepted the invitation "in furtherance of my commitment to cooperate and provide the American people with answers". But federal prosecutors recommended a "substantial term of imprisonment" for Cohen, saying he "repeatedly used his power and influence for deceptive ends" and claiming that his cooperation with Mueller was "overstated".
It was not immediately clear whether prosecutors in NY or for Mueller would ask Cohen to keep from discussing topics still under investigation.