The Egyptian authorities had accused Qatar-based Al-Jazeera of acting as a mouthpiece for the Muslim Brotherhood.
The station denied the accusation and said the journalists were just doing their job.
Greste and Fahmy were sentenced to seven years' jail, while Mohammed got three years more, because he was found with a spent bullet casing.
Rights groups dismissed the trial as a sham and foreign countries, including Australia and the United States, expressed their concern over the journalists' detention.
Last night, Peter Greste's mother, Lois, said the appeal court's ruling was "not as good as we hoped".
Adel Fahmy, Mohammed Fahmy's brother, said he had hoped his sibling would be freed.
He said each lawyer received just three minutes to argue his case.
There had been expectations the journalists would be released amid a thawing of Cairo's ties with Qatar.