Michael Adebolajo and Michael Adebowale have been found guilty of killing drummer Lee Rigby.
The pair were cleared of the attempted murder of a police officer.
After the murder, Adebolajo had charged at a marksmen wielding the cleaver while Adebowale brandished a gun.
The jury took around 90 minutes to come to their decisions.
Relatives of Fusilier Rigby broke down in tears as the verdicts were given.
Mr Justice Sweeney ordered that the decisions be heard in silence.
He said he will pass sentence after a key appeal court ruling on the use of whole life terms in January.
As the jurors were thanked for their service, Mr Justice Sweeney said: “It’sno doubt a case that is going to stay with us all for a long time.”
As the defendants were taken down, Adebolajo kissed his koran and raised it in the air.
The judge expressed his “gratitude and admiration” for the soldier’s family.
He said they had “sat in court with great dignity throughout what must have been the most harrowing of evidence”.
The judge added: “I’m extremely grateful to them and can only sympathise with what has happened to them and its continued effect … upon all their lives.”
Fusilier Rigby’s family and friends, including his widow Rebecca, sat through weeks of harrowing evidence on the final movements of the soldier and his killers.
Disturbing video footage of the soldier being run over by the Vauxhall Tigra, driven by his murderers at 30-40mph, was shown, as were clips of the two extremists dragging his limp and bloodied body into the middle of Artillery Place outside Woolwich barracks.
Adebolajo pulled Fusilier Rigby’s head to the side and attempted to decapitate him, while Adebowale stabbed him repeatedly.
One witness described their actions, which took place just yards from Mulgrave Primary School, as being “like a butcher attacking a joint of meat”.
The men had armed themselves with eight knives, including a meat cleaver and a five-piece set bought by Adebolajo from Argos the previous day.