Gary Vinter, 42, picked a high-profile target in July 2011 because he wanted to change the conditions in which he was held at Wakefield jail, West Yorkshire.
Roy Whiting, a convicted sex offender sentenced to life in prison in 2001 for the murder of eight-year-old Sarah, received emergency care following the attack in his cell and has recovered.
Vinter appeared via a videolink from Long Lartin Prison, Worcestershire, before Mr Justice Openshaw, sitting at Newcastle Crown Court. He said: "He was a dirty little nonce. That's why I did it."
Vinter, from Middlesbrough, sneaked into Whiting's cell and used a sharpened plastic toilet brush handle to stab Whiting in both eyes. Vinter then kicked and punched Whiting as he lay on the floor.
Vinter, serving a whole- life sentence after murdering a workmate in 1996 and his estranged wife in 2008, picked out Whiting for his notoriety, the court heard.
He admitted wounding with intent and was given an indefinite sentence, with a notional minimum term of five years.