Kevin Hyden was already serving a life sentence for the brutal 2014 murder of his neighbour Davinia Loynton in Wellington but has now had an extra five years added to his existing 32-year minimum term behind bars.
The 40-year-old attacked Whiting with fellow murderer Richard Prendergast while shouting "get him in the neck" and calling him a "nonce".
Whiting - who was jailed for life in 2001 for the abduction and murder of eight-year-old Sarah Payne - was targeted in his cell on D wing of Wakefield Prison in November 2018, Leeds Crown Court heard.
Hyden, 40, used a screw to attack Whiting while Prendergast, 40, armed himself with two pieces of wood with a 6.7cm screw sticking out between them, a judge was told on Wednesday.
Prosecutor Jonathan Sharp said one of the lifers shouted "you f****** nonce" as they stabbed and punched him multiple times on November 8, 2018.
One also screamed: "Stab him, stab him, get him in the neck."
Mr Sharp said Whiting was pulled up by the hair and the one-minute beating continued until prisons officers arrived with batons.
Whiting suffered puncture wounds all over his head, neck and upper body.
Judge Tom Bayliss QC jailed the pair for an additional seven-and-a-half years, and said the practical effect of this - as they would normally only serve two-thirds of the sentence - was for five years to be added on to the minimum terms they must already serve before being considered for release.
Brutal Wellington murder
Hyden was jailed for life with a minimum term of 32 years after he tortured and killed Davinia Loynton who lived next door to him as he looked for money for drugs.
The addict forced his way into the 59-year-old's flat in Glebe Street, Wellington, and tortured her as he tried to get cash for drugs before killing her.
Miss Loynton was found rolled up in her living room rug at her flat by distraught friends and colleagues after she failed to show up for work at at Serchem Ltd in Telford, where she had worked for almost 30 years.
Prosecutors said Hyden tortured his victim to reveal the PIN numbers to her bank cards before smashing her skull in, cutting her throat and leaving her with injuries normally associated with a car crash.
He withdrew more than £2,700 from her bank accounts in just two days, using the cash to buy hundreds of pounds worth of cocaine.
Hyden was on licence from prison at the time of the killing after being released from a six-year sentence imposed after he attacked an antique dealer with a hammer.
He had also admitted burgling Miss Loynton just nine months before her death, again while he was on licence from prison.
Despite a mountain of evidence showing Hyden was the killer, he consistently denied his involvement and was eventually found guilty at trial.
'His notoriety is irrelevant'
Whiting is himself serving a life sentence with a minimum 40-year term for the abduction and murder of Sarah Payne, who disappeared while playing near her grandparents’ home in Kingston Gorse, West Sussex, in 2000.
Her body was found in nearby Pulborough 17 days later.
Both Hyden and Prendergast admitted causing Whiting, 61, grievous bodily harm with intent earlier this week.
The prosecutor said Hyden commented he had "done what everyone else wanted to do" and boasted about his actions but this could have been "opportunistic bravado" to enhance his status in the maximum security jail.
He said Prendergast later tried to justify his actions by saying he wanted to be moved from D wing because it was associated with offenders against children, which he was not.
Judge Bayliss said: "Whatever may have been his crime, whatever may have been, and remains, his notoriety, that, in my judgment, is irrelevant other than to record that his notoriety seems to have served as something of a motivation for the two of you to have done what you did."
He said the pair had not even spoken to Whiting before the incident.
The judge said it did not matter whether the defendants were motivated by a desire to move wings or the "inexplicable kudos".
He said: "None of that matters. What matters is that the two of you together formulated a plan to attack a fellow prisoner."
The judge said it was a "serious and sustained assault".
Whiting has been attacked a number of times in prison.
In 2011, double murderer Gary Vinter stabbed him in the eye twice, also in Wakefield Prison, because he was a "dirty little nonce", a court heard at the time.
Prendergast, from Worksop, Nottinghamshire, was jailed for life with a minimum term of 19 years in 2018 for murdering 44-year-old Lee Moody, who he falsely accused of stealing his mobile phone.
Witnesses said Prendergast picked up a knife from a kitchen drawer and stabbed Mr Moody after he got angry about his missing mobile phone and mistakenly thought Mr Moody had stolen it.
Judge Bayliss heard on Wednesday that Prendergast has convictions for 53 separate offences and Hyden has 125.
No victim impact statement from Whiting was presented to the court.