Comey's highly-anticipated testimony, which will be slated after the Memorial Day congressional recess, comes after he was sacked by Trump May 9 amid a mounting investigation into Russian involvement in the 2016 election and possible ties between Trump campaign associates and the country.
The Russian government is accused by U.S. intelligence of trying to tilt the 2016 election in Trump's favor.
Trump, accompanied by wife Melania, walk across the South Lawn of the White House in Washington on Friday.
On Thursday, Trump declared himself the victim of the "greatest witch hunt" in American political history and denied allegations of collusion.
"The committee looks forward to receiving testimony from the former director on his role in the development of the intelligence community assessment on Russian interference in the 2016 U.S. elections", Burr said in a statement, "and I am hopeful that he will clarify for the American people recent events that have been broadly reported in the media".
Mr Comey's ouster followed requests from the President that he stop an investigation into former National Security Adviser Michael Flynn, who was forced to resign for misrepresenting a conversation he had with Russian officials to Vice President Mike Pence.
The White House was rocked by a further revelation Friday, when reports emerged that Trump said his sacking of FBI director James Comey has relieved "great pressure" on him caused by the Russian Federation investigation.
If the White House couldn't get Mueller removed, they'd use the rule to cast doubt on his impartiality, according to Reuters:"Under this strategy, the sources said the administration would raise the issue in press conferences and public statements", Julia Edwards Ainsley reported.
"There is no reason he can't testify before both the Intelligence and Judiciary Committees, particularly given that the Judiciary Committee is the FBI's primary oversight committee", Judiciary Committee Chairman Charles Grassley, R-Iowa, and ranking Democrat Dianne Feinstein, D-Calif., wrote in a statement.
He said the investigation would have always continued, and the termination of Comey would not have ended it.
While not confirmed by the White House, this plan of action would be a major attempt to weaken the investigation into the Trump campaign's possible ties with foreign actors. It says the president then told Russia's foreign minister and ambassador that he "faced great pressure because of Russian Federation".
"By grandstanding and politicizing the investigation into Russia's actions, James Comey created unnecessary pressure on our ability to engage with Russian Federation", press secretary Sean Spicer said in the statement.
Trump has repeatedly slammed the FBI and congressional investigations as a "hoax" and blamed disgruntled officials at intelligence agencies for leaking information related to the probes.
"Once again, the real story is that our national security has been undermined by the leaking of private and highly classified conversations", he added. "I believe it. I stand by it".
Rosenstein ensured House members that the Justice Department would work with members of Congress "to coordinate our parallel efforts" and establish a point of contact for Mueller. Trump aides said he never tried to squelch the Flynn investigation nor made inappropriate disclosures to the Russians.