Kevin McCarthy, 49, had admitted trying to murder Damien Fowkes, 41, in October last year. The attack left Fowkes with life-threatening neck injuries.
Fowkes is serving a life sentence with a minimum term of 20 years for slashing the throat of Huntley.
McCarthy must serve at least 18 more years, Cambridge Crown Court was told.
Both McCarthy and Fowkes were inmates at HMP Whitemoor in March, Cambridgeshire, at the time of the attack.
Peter Gair, prosecuting, said McCarthy grabbed Fowkes from behind and cut his throat with a homemade blade while lunch was being prepared on 2 October 2016.
He said there was no clear motive for the violent assault, but some prisoners had complained about McCarthy not taking his turn to clean the kitchen earlier that morning.
It was the third time McCarthy had tried to murder a prisoner, Mr Gair said.
In sentencing, Judge David Farrell told McCarthy: "This was a premeditated, planned attack... It only failed to kill him because the cut wasn't deep enough."
McCarthy, who appeared by videolink, sipped from a mug during the sentencing and showed no reaction.
He was already serving time for attempted murder, and has convictions stretching back to 1990.
Huntley is serving a life sentence with a minimum term of 40 years for the murders of 10-year-olds Holly Wells and Jessica Chapman in Soham, Cambridgeshire in 2002.
Fowkes is serving a minimum term of 20 years for the attempted murder of Huntley at HMP Frankland in Durham in 2010.
He went on to strangle paedophile and child-killer Colin Hatch in 2011 at HM Prison Full Sutton, a high security unit near York.
A prisoner who slit the throat of a fellow inmate who had himself attempted to murder Soham child killer Ian Huntley has been jailed for life.