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Michael Adebowale, 22, of Greenwich, London, has been remanded in custody to appear at Westminster Magistrates' Court on Thursday morning.
A second man, Michael Adebolajo, 28, remains under arrest at a London hospital.
Drummer Rigby, 25, was stabbed to death in a street attack in Woolwich on Wednesday, 22 May.
Mr Adebowale, who was discharged from hospital on Tuesday, has also been charged with possession of a firearm.
Sue Hemming, head of the Crown Prosecution Service (CPS) Special Crime and Counter-terrorism Division, said: "Crown Prosecutors have been working with the investigators of Counter Terrorism Command since the killing of Drummer Lee Rigby on 22 May.
"Following the release of Michael Adebowale from hospital, we have authorised the police to charge him with the murder of Drummer Rigby.
"We have also authorised police to charge him with possession of a firearm, contrary to section 16A of the Firearms Act 1968.
"There is sufficient evidence to prosecute Michael Adebowale and it is in the public interest to do so. He will appear at Westminster Magistrates' Court tomorrow, Thursday, 30 May."
The CPS said it was continuing to advise police over other suspects arrested during the investigation into Drummer Rigby's death.
A post-mortem examination found that the soldier died of "multiple incised wounds".
Scotland Yard said the inquest into Drummer Rigby's death would open at Southwark Coroner's Court on Friday.
Commander Simon Letchford of the Metropolitan Police has made a fresh appeal for information and witnesses following the incident near the Royal Artillery Barracks in Woolwich.
A minute's silence was held in Woolwich just before 14:20 BST on Wednesday - exactly a week after the event - followed by spontaneous applause.
Drummer Rigby's fiancee Aimee West said she was "devastated by the loss".
The Independent Police Complaints Commission is investigating, which is routine in situations where police officers have discharged their firearms, after two men were shot in the incident.
The commission said two police officers had fired shots and one had used a Taser.
Police have arrested eight other people in connection with the investigation so far; six of these have been bailed and two released without charge.