LONDON—Two British-born, Al Qaeda-inspired extremists who considered themselves “soldiers of Allah” were convicted Thursday of murdering an off-duty serviceman who was run down with a car and stabbed to death in a frenzied attack on a London street.

The jury of eight women and four men deliberated for just 90 minutes before finding Michael Adebolajo and Michael Adebowale guilty of murdering Fusilier Lee Rigby. They were acquitted of attempting to murder a police officer.

The two men will be sentenced early next year.

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Neither defendant reacted as the jury foreman announced the verdicts. Adebolajo, at 29 the elder of the two, smiled and kissed a copy of the Qur’an as he was led down to the cells.

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 passerby 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 defence 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.

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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 centres, and by protests from far-right groups.

Police contrasted the savagery of the attack with the bravery and compassion of passersby. One woman tried to comfort Rigby as he lay in the street. Another tried to persuade Adebolajo to put down his weapons.

Farooq Murad, secretary general of the Muslim Council of Britain, called the murder a “barbaric act.”

“Muslim communities then, as now, were united in their condemnation of this crime,” he said.

Prime Minister David Cameron welcomed the guilty verdicts on the murder charge. He said the crime “shows 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.”

The attack raised questions about whether Britain's intelligence services could have done more to prevent Rigby's killing, as both suspects had been known to them from earlier inquiries.

Adebolajo, who comes from a Christian family and converted to Islam in his teens, was arrested in November 2010 near the Kenya-Somalia border and eventually returned to Britain. Kenyan officials said he intended to join an Islamic militant group in Somalia.

The pair had been radicalized, in part through exposure to firebrand preachers like U.S.-born Al Qaeda leader Anwar al-Awlaki, who was killed in a U.S. drone strike in Yemen in 2011. Sermons by al-Awlaki and other extremist material were found at Adebolajo's father's house.

The men were not accused of being linked to a wider conspiracy. Adebolajo told the court he had never met anyone from Al Qaeda but admired the terrorist group and considered its members his “brothers in Islam.”

The judge praised the dignity of Rigby's family “throughout what must have been the most harrowing of evidence.” He thanked jurors, who sat through graphic footage of the murder, for their service.

The judge said he would sentence the defendants next year, after a January Court of Appeal ruling on the use of life sentences without parole.

The Crown Prosecution Service said it would ask the court to find that the murder was motivated by terrorism, which could add to the length of the sentences.