Michael Adebolajo, 29, and Michael Adebowale, 22, struck Fusilier Rigby with a car before hacking him to death.
Adebolajo had claimed he was a “soldier of Allah” and the killing was an act of war.
The men were found not guilty of attempting to murder a police officer at the scene.
‘Family in tears’
The Old Bailey jury of eight women and four men took approximately 90 minutes to reach its verdict.
They had heard that Adebolajo and Adebowale drove a car into Fusilier Rigby at 30-40mph, before dragging him into the road and attacking him with knives and attempting to decapitate him with a meat cleaver.
Relatives of Fusilier Rigby broke down in tears as the verdicts were given.
His wife said the family was satisfied that justice had been done, adding: “This has been the toughest time of our lives. No one should have to go through what we have been through as a family.”
Rebecca Rigby said: “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.”
Mr Justice Sweeney ordered that the decisions be heard in silence. He said he will pass sentence after a key appeal court ruling on the use of whole life terms in January.
‘Sickening and barbaric’
Prime Minister David Cameron said: “The whole country was completely shocked by the murder of Lee Rigby and the whole country united in condemnation of what happened and I’m sure everyone will welcome these verdicts.
“We have to redouble our efforts to confront the poisonous narrative of extremism and violence that lay behind this and make sure we do everything to beat it in our country.”
Home Secretary Theresa May said the “sickening and barbaric” murder of Fusilier Rigby “united the entire nation in condemnation”.
The BBC’s June Kelly looks back at how events in Woolwich unfolded
Assistant Commissioner Cressida Dick, the head of the Met’s specialist operations, said justice had been done.
“This horrific attack, which took place in broad daylight on the streets of London, shocked the country and was intended to divide communities. It had largely the opposite effect and has, in fact, brought people together,” she said.
The jury heard the men chose their victim because he was “the soldier that was spotted first”.
In a police interview Adebolajo said he and Adebowale decided to lie in wait near the barracks and targeted Fusilier Rigby because he was wearing a Help for Heroes hooded top and carrying a camouflage rucksack.
The attack occurred on a busy street, witnessed by shocked onlookers. A number of women – such as Amanda Donnelly-Martin – approached Fusilier Rigby, who was lying in the road, and attempted to comfort him, but he was already dead.
Adebolajo handed Ms Donnelly-Martin a handwritten letter containing a speech about fighting “Allah’s enemies” and bringing “carnage” to London’s streets.
The murderers were also armed with a gun – 90 years old and unloaded – which they used to frighten off members of the public before armed police arrived at the scene.
As a police vehicle approached, both men rushed towards it, with Adebolajo raising the meat cleaver above his head and Adebowale waving the firearm.
Both men were shot by police in scenes captured by CCTV. Officers then administered first aid on the two men before they were taken to hospitals in south London.
The two men denied attempting to kill police, saying they had wanted armed officers to shoot them dead so they could “achieve martyrdom”.
Now that’s what I call crazy. May God forgive us all.
p class=”post-sig”>Its Parker baby