Robert Bryan, 43, died in hospital after he was attacked by Kieron Simpson, 26, at HMP Doncaster on 27 February.
A post-mortem examination found the cause of death was a blow to the head.
Simpson, from Dodworth, was serving a sentence for burglary when he attacked Bryan. He admitted manslaughter at Sheffield Crown Court on 30 April.
The court heard Bryan, who was serving a sentence for manslaughter, was knocked unconscious when he fell to the floor after being struck by Simpson. He died later the same day.
Det Sgt Andrew Knowles said: "This case clearly shows how dangerous and devastating just one punch can be.
"Simpson attacked Bryan for no apparent reason - he may not have intended to kill him but anyone who makes the decision to strike another with force must consider the potential shattering consequences a single punch can have."
A man has been jailed for four years for killing an inmate with a single punch at a South Yorkshire prison.