Lotfi Raissi, 29, who has also filed separate claims for a reported £13 million ($21.6 million) against the US Federal Bureau of Investigation (FBI) and the US Justice Department, won his case against Associated Newspapers, publishers of the Mail on Sunday, which printed the unfounded US allegations.
Louis Charalambous, Raissi's lawyer, told the court the Mail on Sunday published an article on 30 September 2001 which referred to allegations made by Washington - in particular that Raissi trained some of the hijackers who flew passenger aircraft into the World Trade Centre and the Pentagon in 2001.
Raissi, a British-based Algerian who studied at a flight school in Arizona, was arrested in London 10 days after the attacks and held for five months in the city's high security Belmarsh prison.
But he was later cleared of wrongdoing in extradition proceedings in front of a British judge, who said US officials had failed to present any evidence to back up accusations that he had links to terrorism.
The Mail on Sunday article also alleged Raissi had dishonestly used the social security number of a dead grandmother to establish a false US identity.
The court said the paper now accepted that, as found during the extradition hearing, "there was no evidence whatsoever to support the contention that Mr Raissi had been involved in the September 11 conspiracy."
"I can't fly aeroplanes anymore. I've been blacklisted from all airlines"
His flying career is in tatters, thanks to the publicity surrounding his arrest."I can't fly aeroplanes anymore. I've been blacklisted from all airlines," Raissi told the BBC.
Timothy Pinto, lawyer for the Mail on Sunday, said the newspaper apologised to Raissi for any distress caused.
His lawyers said in a statement he and his wife were "pleased to have got vindication of their reputation from a section of the media which failed to treat him fairly whilst wild accusations were being levelled at him by the US government and in the extradition proceedings."
"Now he can start to rebuild his life by restoring his good reputation through the courts both here and in the United States, where he has commenced proceedings against the FBI and the US Department of Justice," the statement said.
He is claiming damages from those US agencies for false imprisonment and malicious prosecution.