The court's decision cannot be appealed. The suspect, Hamdi Issac, is expected to be transferred to Britain within the next 10 days, said Paolo Iorio, a lawyer representing the British government in the case.
"The request of the British government has been accepted," Iorio told reporters after the hearing.
Issac was not in court, and awaited the ruling in the Rome prison where he is being held.
A Rome court last month ordered Issac to be extradited to Britain. His lawyer filed an appeal, citing what she said was lack of proper documentation by the British authorities and saying Issac feared "heightened tension" in Britain might affect proceedings there against him.
Issac's lawyer, Antonietta Sonnessa, did not immediately comment Tuesday, saying she wanted to read the ruling first.
Issac, a British citizen also known as Osman Hussain, was arrested on an international arrest warrant in the Italian capital on July 29. Through his lawyer, he had said he wanted to remain in Italy.
British authorities want to prosecute Issac for his alleged role in the attempted bombing at the Shepherd's Bush subway station, one of four botched attacks on London's transport system July 21. Nobody died in the attacks.
In her appeal, Sonnessa complained that she had not received a report from the British analyzing the contents of the bag that Issac allegedly carried onto a subway at Shepherd's Bush station on the day of the attacks.
Through his lawyer, Issac has said his bag contained a mixture of flour and a liquid hair product and that the attack was not meant to kill.
The botched attacks came two weeks after suicide bombings on London's transport system killed 52 people and the four bombers.