Homosexuality is not specifically banned under Egyptian law, so the men, arrested in September, were charged with "inciting debauchery and offending public morality."
The court also sentenced the eight to three years of probation once they have served their terms.
The video, filmed aboard a Nile riverboat, shows what prosecutors said was a gay wedding ceremony, with two men in the centre kissing, exchanging rings and cutting a cake with their picture on it.
One of the defendants, prior to their arrest, told a television talk show that the video was recorded during a birthday party.
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At the last hearing, on October 11, a spokesman for the justice ministry's forensics department insisted the men were innocent.
"The medical test showed that the eight defendants have not practised homosexuality recently or in the past," Hesham Abdel Hamed told AFP.
"The entire case is made up and lacks basis. The police did not arrest them red-handed and the video does not prove anything."
HRW has demanded that the men be released.
In the past, Egyptian homosexuals have been jailed on charges ranging from "scorning religion" to "sexual practices contrary to Islam", the country's dominant religion.