Manfu Asiedu, Jewel Uddin and Shah Rahman were found guilty of carrying out the attack on a fellow prisoner in the gym area of the maximum security prison on April 21 last year.
A jury at Leeds Crown Court heard the three men may have attacked convicted murderer Jeremy Green in retaliation after he is alleged to have said to them: “Here come the Taliban.”
The trial heard the attack took place in a corridor leading from the gym.
The three men began punching and kicking Green and continued to attack him as a prison officer tried to intervene.
The prisoner suffered a fractured cheek bone and a broken nose.
Green, 27, a former Army lieutenant, was ordered to serve a minimum of 34 years in prison in April last year for the murder of his ex-girlfriend Nicole Waterhouse and the attempted murder of her friend Karen Browne.
The attack took place at Miss Waterhouse’s home in York in York in October 2013.
During a nine-hour ordeal he tortured, stabbed and smothered them while texting messages purporting to come from them. Prosecutors said he stabbed both women multiple times, cutting their throats and smothering them with pillows.
Describing the prison attack, Mr Justice Males said: “It is difficult to make any positive finding as to the way in which this attack began, but I accept it is at least possible that there was a degree of provocation by a remark by your victim which sparked off - the comment “Here come the Taliban.”
The judge added: “Even if that is right, there are no excuses for the vicious attack upon Mr Green.”
All three men were found guilty of inflicting grievous bodily harm.
Asiedu is serving a 33-year sentence for his part in helping to plan the failed suicide attacks on London’s transport network on July 21 2005.
Ghanaian-born Asiedu was meant to have exploded his rucksack device but “lost his nerve at the last moment” and dumped it in woodland.
The attacks were attempted two weeks after four British Islamists from West Yorkshire killed 52 people in suicide bombings on three underground trains and a bus in the capital.
Asiedu was given a two-year sentence over the prison attack, to run concurrent to 33-year sentence.
Uddin is serving a 19-and-a-half year sentence for his role in planning to bomb an English Defence League rally in Dewsbury in June 2012.
He was among the gang that had taken a bomb, knives and sawn-off shotguns to the rally. But the plotters arrived two hours after the EDL event had ended. Uddin and the other gang members were caught by chance after a car being used by two of them, and carrying weapons, was stopped by police on the M1 after the rally and found to have no insurance.
Uddin was given a three-year concurrent sentence for the prison violence.
Rahman is serving a 12-year extended sentence for plotting to plant a bomb in the Stock Exchange in London in 2010.
He was also seen scouting other potential targets including Big Ben, Westminster Abbey and the London Eye.
Rahman was given a two-year sentence to run concurrent to the terrorism offence.