Michael Adebolajo, 29, and Michael Adebowale, 22, murdered Lee Rigby, 25, as he returned to the Woolwich barracks in south London, in May.
They were convicted after a trial at the Old Bailey in central London, which heard that the soldier was almost beheaded in the attack.
Adebolajo looked at the press and kissed his Qur’an as he was taken to the court cells.
Adebolajo, from Romford, Essex, and Adebowale, from Greenwich, south London, claimed they were soldiers of Allah and their violence was a reprisal against western foreign policy, which had led to the deaths of Muslims.
At the time of the attack, Rigby was attached to the regimental recruiting team and was on his way back to barracks in Woolwich from a shift working at the Tower of London. Previously he had served a tour of duty in Helmand, Afghanistan, fighting Islamist militants.
His wife, Rebecca Rigby, said: “I would like to thank everyone who has helped us to finally get justice for Lee.
“This has been the toughest time of our lives and no one should have to go through what we have been through as a family. These people have taken away my baby’s dad, but Lee’s memory lives on through our son and we will never forget him.
“I now want to build a future for Jack and make him proud of his dad like we all are.”
The brother of one the killers said the attack was inevitable and the justification for Rigby’s death was obvious. Speaking to al-Jazeera’s Investigations Unit, Jeremiah Adebolajo, who like his brother Michael is a Muslim convert, predicted another Woolwich-style attack due to British foreign policy.
After Rigby was attacked in the street, Adebolajo was filmed on the mobile phones of passersby, justifying the murder as a strike against the west, in language echoing the propaganda of violent jihad.
In the footage, Adebolajo said: “You people will never be safe.”
Brandishing a cleaver and a knife in his bloodied hands, and with the body of Rigby lying metres away, Adebolajo said: “We swear by almighty Allah we will never stop fighting you. The only reason we have done this is because Muslims are dying every day. This British soldier is an eye for an eye, a tooth for a tooth.
Adebolajo decided before one court hearing that he wished to be called after one of the most notorious Islamist extremists in British history. He asked to be addressed as Mujaahid Abu Hamza. His co-accused asked to be addressed as Ismail Ibn Abdullah during proceedings.
The murder raised questions for the security services, who had had both men on their radar.
They had been known to MI5 and the police for eight years but had been assessed as peripheral figures and thus not subjected to a full-scale investigation.
Adebolajo, who was born into a church-going Nigerian family but converted to Islam, had complained of harassment by MI5 in the last three years after he came to the intelligence agency’s attention.
He was detained by Kenyans for suspected extremist activity in 2010 and later deported to Britain, the Foreign Office confirmed.
Adebowale was also a convert to Islam. As a teenager, he witnessed a murder and was himself stabbed in a frenzied knife attack five years ago. He suffered from psychotic episodes caused by cannabis abuse and by the psychological effects of being caught up in the fatal stabbing incident in January 2008, when he was 16.
Both attackers had attended events of the extremist group al-Muhajiroun and, after it was banned, of its successor groups.
Adebolajo and Adebowale face sentences of life imprisonment, with the main issue for the judge being how long a minimum tariff they should serve before they can even be considered for release.
Adebolajo showed no remorse for his actions when he gave evidence in his trial, telling jurors that he was a “soldier of Allah” and that he had no choice but to obey the command of Allah.
Speaking in a low voice only feet from Rigby’s family, Adebolajo described how he held the soldier’s hair as he hacked at his neck in a motion described by one witness as like a “butcher attacking a joint of meat”.
Another horrified bystander said he “instantly believed that he was trying to cut the victim’s head off” when he saw the man using a meat cleaver to mutilate Rigby’s motionless body. A third witness said Adebolajo had a look of pure evil after attacking Rigby’s head while his accomplice rammed knives into his chest like he was “trying to remove his organs from his torso”.