Al Jazeera's acting director general, Mostefa Souag, also released a statement Wednesday, welcoming the release of the two men.
"We’re delighted for them both and their families," the statement said, while adding that it was "hard to celebrate" because "this whole episode should not have happened in the first place."
"They’ve lost nearly two years of their lives when they were guilty of nothing except journalism," Souag said.
He added the network would continue to call on Egyptian authorities to drop convictions against seven of its journalists tried in absentia, including Australian reporter Peter Greste, who was arrested alongside Fahmy and Mohamed.
"The case for seven journalists convicted in absentia continues ... We urge the Egyptian authorities to quash their cases and let them too get on with their lives," Souag said.
"I don't know what to say. It is done. Thank God, thank God," Fahmy's brother Adel told The Associated Press.
Fahmy's lawyer, Khaled Abu Bakr, told the AP that his client was a "professional and innocent journalist," adding that he hopes Egypt's decision will "have a positive impact on the media and international level."
The pardons coincided with Eid al-Adha, the Muslim holiday that starts on Thursday and came a day before Sisi was due to head to New York to deliver a speech at the U.N. General Assembly.
Sisi on his Facebook page announced on Wednesday that he would release "100 young people trapped in issues related to the breach of the law on demonstrations and some humanitarian and health cases."
The Al Jazeera network continues to demand all charges and sentences against its journalists are dropped.
On August 29, a court in Cairo sentenced Fahmy, a Canadian citizen, and Mohamed, an Egyptian citizen, along with Greste, to three years in prison after finding them guilty of aiding a terrorist organization.
Greste was released in February and repatriated to Australia but his court case continued in absentia.
Mohamed was sentenced to an additional six months for possession of a spent bullet casing.
The journalists had been initially found guilty in June 2014 of aiding a terrorist organization — a reference to the Muslim Brotherhood, which was outlawed in Egypt after the army overthrew President Mohamed Morsi in 2013.
At that hearing, another six Al Jazeera journalists were tried in absentia on the same charges and were sentenced to 10 years' jail.
With wire services