The video, obtained by The Sun, shows the Respect MP having a 20-minute meeting with Saddam's eldest son in an Iraqi palace in 1999.
In the video, Galloway is seen to greet Uday, shaking his hand twice and calling him "Excellency."
He jokes about losing weight, going bald and failing to give up smoking cigars.
Galloway also orders watching journalists not to publish parts of their conversation.
Finally, according to the paper, he taunts the U.S. and vows to stick with Uday "until the end".
The video was shot for an Iraqi TV station and was smuggled out of Iraq before the regime fell.
Uday beat and stabbed to death his father's personal valet and food taster, Kemal Hana Gegeo, and was briefly imprisoned by Saddam.He also raped numerous women, and his victims are believed to have included a visiting Russian ballerina.
And as head of the Iraqi Olympic Committee, he oversaw the imprisonment and torture of Iraqi athletes who were deemed not to have performed to expectations.
Uday was shot dead by US soldiers in 2003. He was 39.
Galloway is the favourite to be voted out of the Celebrity Big Brother house this evening.