High Court judges found that there was enough acceptable evidence to facilitate a U.S. trial of Masri and gave the suspect's lawyers two weeks to file a House of Lords appeal of their extradition decision, The Times of London said.
Masri, 51, is serving a seven-year prison sentence for inciting racial violence at a British prison.
He is wanted in the United States on 11 terror charges, including allegedly organizing an al-Qaida training camp in Oregon.
The Daily Telegraph said Masri was the first person to be arrested when a new extradition treaty was reached between Britain and the United States in 2004.
His extradition to the United States was delayed so he could stand trial in Britain and his lawyers attempted to block the extradition by challenging U.S. prosecutors' evidence. His lawyers allege evidence against their client was obtained through the use of torture and should be inadmissible, the Telegraph said.