Mueller will testify before both committees on July 17 about his investigation against alleged Russian meddling in the 2016 US presidential elections, the statement said on Tuesday.
"Americans have demanded to hear directly from the special counsel so they can understand what he and his team examined, uncovered, and determined about Russia's attack on our democracy, the Trump campaign's acceptance and use of that help, and President Trump and his associates' obstruction of the investigation into that attack," said the statement, reported Xinhua news agency.
Mueller concluded his 22-month investigation in March by submitting a report to Attorney General William Barr.
The report stated that there was no evidence that Trump's campaign conspired with the Russian government during the 2016 US presidential election, but didn't conclude if the President had obstructed justice.
Instead, Mueller recounted 10 episodes involving US President Donald Trump and discussed potential legal theories for connecting these actions to elements of an obstruction offense.
The Department of Justice concluded that Mueller did not have "sufficient" evidence to support a charge in the obstruction case, a move that has drawn scrutiny by Democrats.
In the first public remarks on his report in May, Mueller said that if his office "had confidence that the President clearly did not commit a crime, we would have said so."
The US Constitution "requires a process other than the criminal justice system to formally accuse a sitting President of wrongdoing," he added.
Trump has repeatedly dismissed Mueller's probe as a "witch hunt" or a politically motivated attack from Democrats.
( With inputs from IANS )