Members of Rigby's family stood in tears outside London's Central Criminal Court as a police officer read out a statement on their behalf.
"We are satisfied that justice has been done," the statement said. "But unfortunately no amount of justice will bring Lee back."
Adebolajo and 22-year-old Adebowale had pleaded not guilty to murder, though neither denied taking part in the May 22 attack.
The 25-year-old Rigby, a member of the Royal Fusiliers who had served in Afghanistan, was returning on foot to his barracks in south London when he was hit by the car being driven by Adebolajo. As the soldier lay on the ground, Adebowale repeatedly stabbed him and Adebolajo attempted to cut off his head.
One witness described the attack, which took place on a busy street near a primary school, as looking "like a butcher attacking a joint of meat."
Adebolajo was filmed by a passer-by moments later, covered in blood and holding a cleaver and a knife, justifying the attack "because Muslims are dying daily by British soldiers."
"An eye for an eye, and a tooth for a tooth," he said repeatedly on the video.
Adebolajo later told the police, in an interview played in court, that he and Adebowale had decided to kill a British soldier, and Rigby had been targeted because "he was the soldier that was spotted first."
Adebowale, who has suffered mental health issues since his arrest, chose to present no evidence in his defense during the three-week trial. His lawyer, Abbas Lakha, told the jury that his client agreed with Adebolajo's description of the attack as a "military operation" and the two men as soldiers.
After the attack the two killers waited at the scene, and then charged at a police car waving a machete and a gun.
Both men had denied trying to kill a police officer, saying they hoped to provoke police into shooting them. Lakha said Adebowale had brandished a 90-year-old unloaded pistol so he "would achieve martyrdom."
Armed officers shot the two men several times — blowing off Adebowale's thumb as he raised the gun — then gave the men first aid.
The savagery of the crime, Adebolajo's bloodthirsty rhetoric — delivered in a London accent — and the ordinary working-day surroundings all helped make the killing a crime that inflamed fears of Islamic extremist terrorism in Britain. It was followed by a spate of attacks on mosques and Islamic centers, and by protests from far-right groups.
Police contrasted the savagery of the attack with the bravery and compassion of passers-by. One woman tried to comfort Rigby as he lay in the street. Another tried to persuade Adebolajo to put down his weapons.