London's Metropolitan Police said Haroon Aswat was taken from Broadmoor psychiatric hospital west of London and escorted onto a plane by US officials.
Aswat is accused of conspiring with radical cleric Mustafa Kamel Mustafa, also known as Abu Hamza al-Masri, to set up a terrorist training camp in Bly, Oregon, 15 years ago.
Aswat had been fighting extradition since his arrest on a US warrant in 2005, and has been treated for paranoid schizophrenia.
Prosecutors have linked Aswat to Mustafa, long prominent in the British media because of his fiery sermons at London's Finsbury Park Mosque. Mustafa was extradited nearly two years ago and convicted in New York in May of terrorism charges.