Ethiopian-born Hamdi Issac, 27, also known as Osman Hussein, was arrested in Rome a week after the 21 July attacks, which killed no one but brought chaos to London exactly two weeks after four bombers had killed themselves and 52 others in the British capital.
"He will be extradited within 10 days. We have won again," the British government's lawyer, Paolo Iorio, said.
He was referring to the 17 August decision by a Rome court to extradite Issac to Britain within 35 days.
Issac's lawyers appealed that decision, arguing that British authorities had not provided proper documentation and saying the suspect feared heightened tension in Britain could prejudice the case against him.
Issac is accused of trying to blow up a London Underground train at Shepherd's Bush station in west London, one of four failed attacks on 21 July that were a near copy of the 7 July bombings.
The three other suspected bombers, Somali-born Hassan Omar, Eritrean-born Muktar Said Ibrahim and Ramzi Mohammed have been in British police custody since late July.
They are accused of trying to blow up a Victoria Line underground train near London's Warren Street, attempting to blow up the No 26 double-decker bus and trying to set off a device at Oval Underground station respectively.
Issac reportedly told an investigating judge and British police that he only wanted to make a "bang" with his device, made from an agricultural substance, a defoliant and flour, to protest against Western military involvement in Iraq.
The other suspected bombers
remain in British police custody
The suspect has repeatedly said he wants to be tried in Italy, where he has been charged in connection with "international terrorism" and holding false identity papers following his arrest on 29 July at a Rome flat rented by his brother.
Issac, evaded heightened British security measures after the attacks and left London by train on 26 July, travelling to Rome via Paris and Milan.
In early August, he was questioned by three Scotland Yard detectives who had travelled to Rome.
An Italian magistrate who supervised the session said the suspect had cooperated with the police and reiterated his device had not been designed to kill.
According to last month's lower court ruling, Issac said during questioning in Italy that he and his associates met the day before the attacks to prepare the devices.
The document cited British officials as saying they suspected the 21 July bombers used a homemade explosive known as TATP (triacetone triperoxide).
TATP is the explosive that British "shoe bomber" Richard Reid placed in cavities in his shoes before trying unsuccessfully to ignite them on a transatlantic flight in 2001.