An Algerian man, wanted over a bombing on the Paris Metro in 1995, which killed eight, has arrived in France after being extradited from the UK.
Eight people died in the 1995 attack on the Saint Michel Metro station
Two High Court judges rejected Rachid Ramda's claim that moves to deport him earlier this month were legally flawed.
The 35-year-old had fought deportation for 10 years, and was the UK's longest-serving extradition prisoner.
Mr Ramda is accused of helping finance the Metro bombing and of organising and financing several other bombings.
The Home Office had said Mr Ramda had no further right to appeal against his extradition.
Mr Ramda's long legal battle against extradition has caused anger in France.
Mr Ramda faces 23 charges of financing and organising a bombing campaign in France between August and November 1995.
On a separate extradition request, he is accused of being a conspirator in the bombing of the Saint Michel Metro station on 25 July 1995, in which eight people were killed and 87 injured.
He is also alleged to be a financier of Algeria's outlawed Armed Islamic Group (GIA).
The GIA, which fights the government in Algeria, is thought to be responsible for the 1995 bombing campaign.
In April, Home Secretary Charles Clarke made a fresh extradition order on the basis that Mr Ramda, who has been held at London's Belmarsh prison, would receive a fair trial.
That was challenged by Mr Ramda's QC Edward Fitzgerald, who told the High Court the decision was "legally flawed".
The High Court hearing in October, which led to Thursday's ruling by Lord Justice Keene and Mr Justice Poole, was told there was "a real risk of a flagrant denial of justice" in deporting Mr Ramda.
Upholding the home secretary's decision that extradition should go ahead, Lord Justice Keene said: "This court is not persuaded that the secretary of state failed in his decision of 5 April 2005 to exercise properly his powers to order the claimant's return to France."
In 2002, two High Court judges quashed an extradition order, signed by the then Home Secretary David Blunkett, and ordered the case be reconsidered.
The judges had expressed concern that evidence against Mr Ramda came from co-defendant Boualem Bensaid, said by his lawyers to have been tortured during interrogation while in French custody.
Altogether, there have been nine separate legal proceedings to extradite Mr Ramda.
The case was brought under the 1989 Extradition Act, which has now been repealed.
It is unlikely that the current extradition provisions would give rise to such a lengthy process.
Supporters of a campaign to block the Algerian's extradition say he could eventually deported from France to Algeria where, they claim, he could face execution.