Michael Adebolajo, 29, and Michael Adebowale, 22, ran over Fusilier Lee Rigby near his barracks at Woolwich in southeast London with a car being driven at about 65 kmph before hacking him to death with knives and a meat cleaver.
The jury of eight women and four men took approximately 90 minutes to deliver a guilty verdict against the two men, both British citizens, following which relatives of the soldier broke down in tears.
The men were found not guilty of attempting to murder a police officer at the scene.
The men did not react when the jury's foreman announced the verdicts. Adebolajo looked at the press, smiled and kissed his Quran as he was taken to the court cells.
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Justice Nigel Sweeney said he would pass the sentence next year after a key appeal court ruling on the use of whole life terms in January.
The two convicted killers grew up in Nigerian Christian families before converting to Islam. Both had a history of petty crime for which they had spent time in jail.
"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."
In Brussels, British Prime Minister David Cameron told reporters: "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.