Lee Newell, 52, also suffered a fractured skull and a severe brain injury in the assault by double killer Gary Vinter at HMP Woodhill, Milton Keynes in November 2014.
Newell had claimed the Ministry of Justice (MoJ) did not protect him.
High Court Judge Peter Marquand found the MoJ breached “its obligation to keep the claimant reasonably safe”.
At a hearing in February, the High Court had heard how Vinter had punched Newell to the ground before repeatedly punching and kicking him in the head, to engineer a move to another prison.
Newell’s barrister Nick Armstrong said Vinter had “a particular history of attacking other prisoners in order to achieve things he wanted”.
In 2011, he had stabbed Roy Whiting, the killer of schoolgirl Sarah Payne, with a sharpened toilet brush handle.
The court heard that in the weeks before the attack, Vinter repeatedly threatened prison staff including warning one officer if he was to tell him he could not move prisons he had “better do it from behind a shield”.
Jack Holborn, representing the MoJ, said Vinter’s threats had been “of a general nature” and “were a not uncommon tactic among violent prisoners”.
He said Newell and Vinter were “dangerous and violent men”, but the MoJ could not keep them “permanently locked up and segregated”.
Newell is currently serving a whole-life term for the murder of child killer Subhan Anwar at HMP Long Lartin, Worcestershire, in 2013.
That crime was committed while serving life for a 1988 murder.
Vinter was jailed in 1996 for the murder of a work colleague and given a whole-life tariff for killing his estranged wife in 2008.
He was given a third life sentence for attempted murder over the attack on Newell.
In a ruling on Wednesday, Judge Marquand said: “The conclusion that should have been reached was to take steps to remove Vinter’s association with other prisoners.”
He awarded Newell £85,000 in damages and £7,000 in interest.