Before being sentenced at the Old Bailey in London, Ian Mytton had pleaded guilty to the manslaughter of Michael Dye.
The 44-year-old Cardiff native died from head injuries after his skull was fractured before a 2012 European Championship qualifier in September.
Judge Stephen Kramer told the court that Mytton's attack on Dye was "unprovoked."
Kramer said Dye was "poleaxed" from the force of the punch and fell backward without trying to stop himself, hitting his head on the ground and suffering "massive brain damage."
Mytton had drunk five pints of beer that day and was holding a can of cider as he and five friends approached Dye.
The 41-year-old Mytton, who is from Worcestershire in central England, is set to be released on license after serving half of his three-year sentence.
"His remorse for what he did and the suffering he caused them (the Dye family) is real, genuine and heartfelt," said Mytton's lawyer, Simon Stirling.
Stirling said Mytton had no previous convictions and had not been involved in football violence before.
England beat Wales 1-0 in the match.