In dramatic scenes, the pair erupted in a violent outburst in the dock after the judge told them their actions were a "betrayal" of Islam.
Mr Justice Sweeney said: "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."
Adebolajo began shouting "Allahu Akbhar", while Adebowale shouted: "That's a lie", and: "It's not a betrayal of Islam".
Referring to Britain, Adebowale screamed: "You and America will never be safe".
The family appeared visibly distressed as the killers could be heard continuing to shout and bang in the cells while the judge continued to sentence them in their absence.
He said: "What the two of you did resulted in a bloodbath.
"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."
He said that the pair had shown "no regret" for the "barbaric" murder, which he said was connected to terrorism.
Passing a whole life tariff for Adebolajo, the judge said there was no mitigation for his actions, and "no hope" of rehabilitation.
In a statement read by family liaison officer Detective Inspector Pete Sparks, the Rigby family said: "We would like to thank the judge and the courts for handing down what we believe to be the right prison terms.
"We would also like to thank everyone who has supported us in the last nine months.
"It has brought us a lot of comfort and we feel satisfied that justice has been served for Lee. We now ask to continue to grieve in private."
Three people were arrested outside the court amid tense scenes as the EDL mounted a protest against the killers.
A bloodstained Adebolajo then approached onlookers and encouraged them to film him on their mobile phones as he ranted about Islam.
Today's sentences comes after a key appeal court ruling last month found that whole life jail terms can be used by UK judges.
Mr Justice Sweeney waited until after the decision to sentence the British-born pair, who were found guilty by a jury in December.
Adebolajo has lodged an application to appeal against his conviction, claiming that his trial was unfair.
Giving evidence at the Old Bailey, he said that he and his accomplice were "soldiers of Allah" and had carried out the sickening killing as revenge for abuse of Muslims abroad.
He said that they chose Fusilier Rigby, 25, as their victim because he was wearing a Help for Heroes hooded top that day.
Referring to the aftermath of the killing, she said: "I couldn't go out or do anything. I felt like I didn't want to go on. I saw people nudging and looking at me if I tried to walk down the street, it was surreal.
"Of all the feelings I have, the one thing that overrides everything is that I know my son will grow up and see images of his dad that no son should ever have to endure, and there is nothing I can do to change this."
Thanking the public for their "overwhelming" support, Mrs Rigby said that she had accepted her husband would be at risk when he went to serve in Afghanistan, but not in Britain, where he was based when he died.
She added: "When you wave someone off you accept that there is a chance you will never see them again. You do not expect to see this on the streets of the UK.
"Lee will never be forgotten. We will always love him and miss him every day."
The court also heard part of a statement from the soldier's stepfather, Ian Rigby.
He said: "After all he had been through in Afghanistan, all Lee was doing was just walking through London. Just seeing on the television and seeing the violence of it you just can't comprehend.
You take it all in and it doesn't click in your head, it is like being somewhere else.
"You're watching it without being actually there."
Sue Hemming, Head of Special Crime and Counter Terrorism at the CPS, described the killing as "one of the most appalling terrorist murders I have seen."
Speaking after the sentencing, she added: "Not only was the attack brutal and calculated, it was also designed to advance extremist views.
"As a solider, Fusilier Lee Rigby was targeted in a clear act of revenge, deliberately carried out in full view of members of the public for maximum impact.
"This attack was always going to fail in that purpose as it served only to bring people together in shock, sympathy and solidarity."
He said: "The scale of the impact on them of the nature of the murder of Lee Rigby in the circumstances made so public during the trial and after such a killing causing a son to pre-decease his parents and stepfather and leave those others who loved him without a husband or a soul mate is too obvious to set out in detail.
"He had, as your lordship knows, a young son. All their lives have been irreparably changed for the worse."
Lee Rigby was described as loving and gentle to his family, and good humoured and dependable to his fellow soldiers.
His murder came after he had survived a bloody and gruelling tour of Afghanistan, from which seven of his comrades did not return.
Adebolajo was raised as a Christian, but converted to Islam while he was a student at the University of Greenwich, before trying to join jihadis in east Africa.
In the shocking footage taken just after the murder, he was seen ranting about how Muslims in other countries had to witness similar horrors to that which he and Michael Adebowale had wreaked in south-east London.
His Nigerian parents work as a nurse and a social worker.
Adebolajo told the Old Bailey jury that most of his friends growing up in Romford were white British, including his best friend Kirk Redpath, who later died fighting with the British Army in Iraq.
He said that he blamed Tony Blair for Mr Redpath's death.
In a police interview he told officers a there was a "war between the Muslims and the British people" and he was a "soldier of Allah".
Mr Gottlieb said: "He should not in these circumstances be deprived of any hope of release."
The barrister said Adebolajo, who has two children and four step-children, was "not someone incapable of change without proper encouragement".
He added: "There's evidence he can be rehabilitated now, not much evidence but some evidence."
Michael Adebowale, whose father works for the Nigerian High Commission and whose mother is believed to be a probation officer, attacked three police officers during his first 24 hours in custody, it can now be reported.
He was said to be "very unpredictable" while in custody, leading to the rare step of allowing him to be handcuffed while in the dock because of the risk he posed to police, prison and security officers.
After being taken to prison in the wake of the killing, he punched a police officer in the face when they tried to stop him picking out his stitches.
During his first police interview, he spat in an officers face, and in a further incident he spat in a glass of water and threw it in a police officers face.
As a teenager, he was the victim of a knife attack in which his best friend died, and told psychiatrists that he was haunted by the voices of his attackers.
He did not give evidence during the trial.
In footage taken at the time of the murder, Ingrid Loyau-Kennett, a French-born mother of two, could be seen remonstrating with Adebowale as he clutched a bloody knife.
She and two other women seen sitting by Fusilier Rigby's side - Gemini Donnelly Martin and her mother Amanda Donnelly Martin - would later be dubbed the Angels of Woolwich for their brave actions on that day.
Reacting to the sentence, Ms Loyau-Kennett appeared to defend Adebowale.
She said: "The 29 year-old getting life is good because he is a killer, but I am more shocked for the other one.
"As far as I am concerned he was dragged in to it. There was no blood on him. He was part of the plot but he did not really take any action but he has got 45 years.
"Add the word terrorism and it marks it up.
"It is so sad for the 22 year old. He was so vulnerable, very shy, he could not speak, he was shaking his head. It's a bit shocking."