"His resolve and willpower ... was very obvious this morning as he looked forward to going back to his normal life."
An Egyptian government spokesman said Mubarak would address the nation by the end of the week.
A statement by Egyptian authorities said he left intensive care at the Heidelberg hospital last Wednesday, and that tests showed he did not have cancer.
Speculation over health
The release of the video comes after a swirl of rumours and speculation over his health, after a marked lack of pictures following his surgery on March 6.
Amr El-Kahky, Al Jazeera's correspondent in Egypt, said news of Mubarak's improvement gave a boost to Cairo's main stock market index, which bounced back from a six per cent loss over the past two days.
Mubarak, who has never appointed a vice-president since he took over in 1981, handed powers temporarily to his prime minister, Ahmed Nazif, before the operation.
He has not said whether he will run again for a sixth six-year term in the 2011 presidential election.
Many Egyptians believe that if he does not, he will try to hand power to his politician son, Gamal, 46. Both Mubaraks deny any such plan.
In 2005, Mubarak allowed multi-candidate elections which he won overwhelmingly, but election observers said at the time there were irregularities in the polls.
In parliamentary elections the same year, police closed down polling stations and judges who oversaw the election said some results were rigged in favour of government candidates.
Opposition groups in the country command little power, but dissidents have been galvanised by a new reform group founded by Mohammed ElBaradei, the former head of the UN nuclear agency.
Last month, ElBaradei flew to Cairo to a rapturous welcome from supporters and formed the National Association for Change.
He has said he is prepared to run against Mubarak in the 2011 presidential election.