Michael Adebolajo, 29, and Michael Adebowale, 22, hacked to death soldier Lee Rigby as he walked back to his barracks in Woolwich, southeast London, in May.
The trial heard that the pair had run 25-year-old Rigby over with a car before attacking him with knives.
Adebolajo had attempted to behead Rigby with a meat cleaver in front of horrified passers-by.
The defendants, both Britons of Nigerian descent, said they committed the murder to avenge the deaths of Muslims abroad and had acted as “soldiers of Islam”.
The jury at the Old Bailey court in London took little more than an hour to convict them.