Kevin Hyden and Richard Prendergast planned the joint attack on the 60-year-old, bursting into his cell each armed with a shank and stabbed and punched him in the head, neck chest and back, Leeds Crown Court was told.
Whiting, who was jailed in 2001 for murdering eight-year-old girl Sarah Payne, was rushed to Leeds General Infirmary but suffered no lasting injuries.
Hyden and Prendergast, both of whom are also serving life sentences for murder and appeared via video link from prison, admitted charges of attempted murder.
Prosecutor Jonathan Sharp said that Prendergast carried out the vicious attack in an attempt to be removed from D-Wing at Wakefield Prison, claiming that other prisoners presume those living on the wing, like Whiting, have committed crimes against children despite neither defendant having done so.
He suggested that Hyden, 40, carried out the attack to enhance his reputation by murdering Whiting, who is loathed by fellow prisoners.
Prendergast, 39, arranged to get a weapon from another prisoner, then discussed his plan with Hyden.
At around 5.15pm on November 8, 2018, Whiting collected his evening meal and went back to his cell.
At 6.12pm, the defendants climbed the stairs to Whiting's landing before bursting into his cell, calling him a 'nonce' and began stabbing and punching him to his head.
Hyden was heard to shout: "Stab him, stab him, get him in the neck!"
Whiting then fell to the floor but was pulled up again by his hair and they continued stabbing and punching him.
Officers, with batons drawn, were eventually able to get into the cell and restored order.
The frenzied attack lasted for about one minute, the court was told, and that Hyden hit him with such ferocity that the nail from his shank snapped off during the frenzied assault.
Whiting sustained multiple injuries and the air ambulance was initially called, although he was taken to LGI by conventional ambulance.
Mr Sharp said that both defendants had lengthy criminal convictions and both are Category A prisoners, serving life sentences for murder.
Prendergast was jailed for a minimum of 19 years in 2018 for stabbing a man to death in Worksop, Nottinghamshire, following a row over a stolen mobile phone.
Hyden is serving a minimum 32-year sentence for torturing and murdering a woman in her own home in Shropshire for drug money in 2014.
Barristers for both defendants offered little in the way of mitigation as to why they had carried out the attack on Whiting, but asked the judge to take into account the ages of the pair when they will be eligible for parole.
Judge Tom Bayliss QC said that whatever their reasoning behind the attempt on Whiting's life, whether it was to engineer a move from D-Wing or for "inexplicable kudos" among fellow prisoners, was irrelevant.
Jailing them each for a further seven-and-a-half years each, he said: "This was a serious sustained assault, it was premeditated and with weapons.
"This is not simply using a weapon that came to hand , this was a case of arming yourselves and bringing them through the prison."