He has been kept in the US since his arrest there in December 2001 when the plane landed.
He was caught after passengers noticed him trying to light his shoes on board the flight from Paris to Miami.
When he was sentenced, Reid shouted at the judge saying:
"I pledge to Osama bin Laden. I'm an enemy of your country."
Experts reckon his shoes were packed with so many powerful explosives, it could have blown a hole in the plane and killed all 197 people on board.