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.
The Old Bailey jury of eight women and four men took approximately 90 minutes to reach its verdicts.
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.
Mr Justice Sweeney ordered that the verdicts be heard in silence. He said he would pass sentence after a key appeal court ruling on the use of whole life terms in January.
He expressed his "gratitude and admiration" for the soldier's family, saying they had "sat in court with great dignity throughout what must have been the most harrowing of evidence".
As the defendants were taken out of the courtroom, Adebolajo kissed his Koran and raised it in the air.
Relatives of Fusilier Rigby broke down in tears as the verdicts were given.
By Frank GardnerBBC security correspondent
How did the police and MI5 miss the Woolwich murderers' switch from legitimate activism to violent jihad? This is one of the key questions being looked at by Parliament's intelligence and security committee, which is expected to report its findings in the new year.
The short answer is prioritisation. Adebolajo made little secret of his extremist leanings and he was clearly 'an individual of interest' to both the Metropolitan Police and the security services, but he was not considered to be planning any attacks.
Many will point to warning signs that suggest they should have paid closer attention to him - he was radicalised by the now-banned group Al-Muhajiroun, and in 2010 he was arrested in Kenya trying to reach Somalia to join Al-Shabaab, the group that this year attacked Nairobi's Westgate mall.
But speaking ahead of the trial - and perhaps predicting some tough questions to come - MI5's director general Andrew Parker defended his organisation's record, saying: "Being on our radar does not necessarily mean being under our microscope."
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."
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".
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.
Lt Col Jim Taylor described the 25-year-old, who was with Second Battalion, the Royal Regiment of Fusiliers, as "a true warrior" and called his death "a cruel tragedy".
"Fusilier Rigby was a highly dedicated and professional soldier. He was one of the true characters within the Second Fusiliers and he is missed greatly," he said.
Farooq Murad, secretary general of the Muslim Council of Britain, said: "Muslim communities then, as now, were united in their condemnation of this crime. This was a dishonourable act and no cause justifies cold-blooded murder."
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".
Meanwhile, an investigation by the Independent Police Complaints Commission (IPCC) has concluded the police officers who shot the men "acted appropriately to the immediate threat" posed.
After studying CCTV footage and mobile footage filmed by a witness "frame by frame, it is incontrovertible that these officers found themselves in an extremely volatile situation confronted by two men, who had just killed someone, armed with knives, a meat cleaver and a firearm in a public place," the IPCC said in a statement.
It added: "It is a testament to the officers' professionalism that once the men were incapacitated they immediately set about providing first aid to them."
The IPCC's findings could not be made public until the conclusion of the trial.
Members of the public have been laying tributes to Fusilier Rigby outside Woolwich barracks near to where the soldier was killed.
Two men have been found guilty of murdering soldier Lee Rigby outside Woolwich barracks in south-east London in May.