Michael Adebolajo was sentenced at the Old Bailey in February alongside Michael Adebowale, who was jailed for life with a minimum term of 45 years.
The pair were sentenced by Mr Justice Sweeney for butchering the 25-year-old father of one in broad daylight near Woolwich Barracks in south east London on May 22 last year.
Heartbroken relatives of Fusilier Rigby said "'justice has been served" after Adebolajo was given the whole-life term, which condemns him to die behind bars.
When announcing the sentences, Mr Justice Sweeney told Adebolajo and Adebowale: "You each converted to Islam some years ago. Thereafter you were radicalised and each became an extremist, espousing a cause and views which, as has been said elsewhere, are a betrayal of Islam and of the peaceful Muslim communities who give so much to our country."
He went on: "You decided between you, and in order to advance your extremist cause, to murder a soldier in public in broad daylight and to do so in a way that would generate maximum media coverage, including getting yourselves killed by armed officers who would be bound to attend the scene in the aftermath of the murder - thereby expecting that you would become martyrs and each gain a place in paradise."
Adebolajo and Adebowale chose the young soldier as their victim because he was wearing a Help for Heroes hooded top, mowing him down in a car before hacking at his limp body with a meat cleaver and knives in an attempt to decapitate him.
Explaining his decision to give Adebolajo a whole-life term, the judge said the 29-year-old, who has two children and four stepchildren, was the leader of the murderous plot and had "no real prospect of rehabilitation".
However, 22-year-old Adebowale's younger age, mental health problems and "lesser role" meant that he escaped spending the rest of his natural life behind bars.