Cohen originally was invited to testify publicly before the House oversight committee on February 7, but postponed the appearance citing verbal attacks against him and his family by Trump and Rudy Giuliani, Trump's current personal lawyer.
Trump and Giuliani last month suggested Cohen's father-in-law should be investigated for alleged but unspecified crimes; the president and his lawyer suggested that Cohen had made up stories about Trump in order to prevent being entangled in a separate potential case.
Cohen will testify before the committee February 27, a day before he talks to the House intelligence committee behind closed doors.
U.S. District Judge William H. Pauley III approved delaying the start of Cohen's three-year sentence until May 6.
"Despite @RealDonaldTrump attacks against his family, Mr. Cohen will not be deterred, will speak about his decade long experiences working for Mr. Trump, his own mistakes and decision to put family and country first", Cohen lawyer Lanny Davis tweeted after the rescheduled hearing was announced.
Cohen was spotted Thursday on Capitol Hill.
While Cohen is expected to address that investigation in his closed-door interviews with the intelligence panels, the chairman of the Oversight panel, Maryland Rep. Elijah Cummings, has set a scope for questioning in an effort not to interfere with Mueller's probe.
The agenda of the hearing does not include any inquiries about special counsel Robert Mueller's investigation into Russian meddling in US elections and possible coordination between 2016 Trump campaign associates and the Kremlin. Federal prosecutors in NY have said Trump directed Cohen to arrange the payments to buy the silence of porn actress Stormy Daniels and former Playboy model Karen McDougal in the run-up to the 2016 campaign. Daniels says she had an affair with Trump.
Cohen acknowledged lying to the committee about his role in a Trump business proposal in Moscow.
It's not clear why Cohen was in the Senate Intelligence Committee's office ahead of his testimony, an unusual step for witnesses who have been interviewed by the panel as part of its two-year Russian Federation investigation.
Michael Cohen - who at one time served as President Donald Trump's personal lawyer and is now preparing for a three-year prison term - is scheduled to testify before the House Committee on Oversight and Reform next Wednesday.
House intelligence committee Chairman Adam Schiff postponed Cohen's appearance before that committee saying it was "in the interests of the investigation", with no additional detail.
He told lawmakers he had abandoned the project in January 2016, but he actually continued pursuing it for months after that.