Salah Helal had been detained in September after being told to step aside during a corruption scandal that prompted the entire government to resign a few days later.
His chief of staff Muhyidin Mohamed Said was also sentenced to 10 years. Helal was also fined one million Egyptian pounds (USD 112,600), and Said was fined 500,000 Egyptian pounds.
The businessman who paid the bribe, and another who facilitated it, were spared jail because they confessed, the official said.
Helal and his chief of staff had been charged with having "requested and received" bribes from businessman Ayman al-Gamil -- via an intermediary -- to legalise the purchase of a property bought from the state.
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The scandal prompted the resignation of prime minister Ibrahim Mahlab's government, with Ismail Sharif replacing him.
Anti-graft watchdog Transparency International ranked Egypt 94th out of 175 nations on its corruption index in 2014.
It says that it has been challenging to assess whether the level of graft has increased or declined because of the rapidly changing context since Egypt's 2011 revolution.
Ahmed Nazif, whom Mubarak sidelined to appease protesters during the revolution that ended his rule, was convicted in a retrial of having used his position to make a fortune of USD 8.2 million.
The court also fined him USD 6.8 million.
Nazif had been accused of corrupt property deals and receiving illegal payments.