Darren McDonald, 40, travelled from Ballymena, County Antrim, to support his team.
At Glasgow Sheriff Court he admitting running on to the pitch after the final whistle and kicking the other man on the head or body.
McDonald was also given a three-and-a-half year football banning order.
He is currently serving a sentence in Northern Ireland and the latest jail term will begin after that ends.
McDonald was named and pictured in the media after the game that saw Hibs beat Rangers 3-2 on 21 May.
Footage from the match was played to the court and newspaper reports from the time were brought to the sheriff's attention.
McDonald was seen clearly wearing a pink T-shirt and had distinctive tattoos.
The unknown Hibs fan was on the pitch after the match and was on the ground, having been assaulted by someone else.
McDonald ran over to him and pulled his right leg back to kick him but slipped and fell backwards.
The court heard that the momentum meant his leg made accidental contact with the Hibs fan's head or body.
He then got up and ran off after the attack, leaving the Hibs fan on the ground.
A Rangers supporter who kicked a Hibs fan during a pitch invasion at last year's Scottish Cup Final has been jailed for nine months.