Ian Rigby, the soldier's stepfather, said: "After all he had been through in Afghanistan, all Lee was doing was just walking through London.
"Just seeing on the television and seeing the violence of it you just can't comprehend. You take it all in and it doesn't click in your head, it is like being somewhere else."
Michael Adebolajo, 29, was given a "whole-life" tariff and Michael Adebowale, 22, was given life with a minimum term of 45 years.
"The Rigby family welcomes the whole life and significant sentences that have been passed down on Lee's killers," a family statement said.
"We feel that no other sentence would have been acceptable and we would like to thank the judge and the courts for handing down what we believe to be the right prison terms."
Adebolajo and Adebowale reacted with fury after being told by Justice Nigel Sweeney their crime was a "betrayal of Islam".
Adebolajo screamed at the judge as he was forced down the dock stairs in the Old Bailey's historic Court No 2. Both men were grabbed around the head by eight officers in the dock.
Adebowale, who also abused the judge, was held to the floor and handcuffed before being carried downstairs head-first. Relatives of Rigby, sitting just a metre from the dock, backed away from the violence, which lasted several minutes.
The judge said the pair became extremists and decided to "murder a soldier in public daylight" to advance their extremist cause. He described the scene as a "bloodbath" and said they "butchered" Rigby.
"I'm sure this was a murder done for the purpose of advancing a political, religious or racial cause. Your sickening and pitiless conduct was in stark contrast to the compassion and bravery shown by the various women at the scene who tended to Lee Rigby's body and challenged what you had done and said."
Last week appeal judges backed British laws ruling that in "exceptional" cases the most heinous criminals can be sent to jail for the rest of their lives. Telegraph Group Ltd