Michael Adebolajo and Michael Adebowale were sentenced at the Old Bailey by Mr Justice Sweeney, who had waited for a key appeal court ruling on whole life terms before deciding the men's fate.
Adebolajo, 29, was given a whole life term while Adebowale, 22, was jailed for life with a minimum of 45 years.
The British-born extremists mowed Fusilier Rigby down in a car before hacking him to death in the street in front of horrified onlookers near Woolwich Barracks in south east London in May last year.
They both claimed that they were "soldiers of Allah" and were motivated by the plight of Muslims abroad to carry out the killing, and have shown no remorse.
After sentencing began the two men shouted at Mr Justice Sweeney in protest at his remarks and were pinned to the ground by several security guards and taken back to the cells.
Mr Justice Sweeney was forced to sentence the men in their absence after they were bundled out of the courtroom following their violent outburst.
Fusilier Rigby's family sobbed as the killers shouted across the historic courtroom, with Adebolajo shouting Allahu Akbhar, and Adebowale calling out "that's a lie" and "it's not a betrayal of Islam" as the judge told them they had been radicalised.
The judge said the pair's behaviour was "sickening and pitiless", and that Adebolajo had no hope of rehabilitation.
"Your sickening and pitiless conduct was in stark contrast to the compassion and bravery shown by the various women at the scene who tended to Lee Rigby's body and challenged what you had done and said."
The struggle in the dock was triggered when the killers, both wearing Islamic robes, reacted angrily to comments that Mr Justice Sweeney made about their extremist beliefs.
He told them: "You each converted to Islam some years ago. Thereafter you were radicalised and each became an extremist, espousing views which, as has been said elsewhere, are a betrayal of Islam."
Adebowale protested that this was a lie, ranting about America and Britain, and his accomplice joined in, screaming "allahu akbar" and hurling abuse at the prison guards who grappled him to the ground.
Both men were grabbed around the face as guards struggled to control them, and taken down to the cells.
The soldier's family were visibly distressed, and one relative needed medical treatment.