Mr Raissi was greeted by family outside court
The United States has abandoned efforts to extradite Lotfi Raissi from Britain on terrorist charges but insists he is still a suspect.
There had been allegations that Mr Raissi, 27, trained pilots involved in the US terror attacks, including the hijackers who crashed a plane into the Pentagon.
District judge Timothy Workman said Mr Raissi, from Colnbrook in Berkshire, could have conditional bail as he only faced extradition on two counts of falsifying an application for a US pilot's licence.
Mr Raissi was released on £10,000 bail, ordered to surrender his passport and told not to apply for international travel documents. He will have to attend London's Bow Street Magistrates Court in March.
'Ridiculous charges'
After the hearing, Mr Raissi's wife Sonia said: "From the beginning we said Lotfi has nothing to do with all this.
"We've said it again and again but at last, justice has been done.
"My message to the FBI is 'You arrested him for terrorism so why do you want to extradite him for these ridiculous, minor charges?'"
Mr Raissi's brother, Mohamed, said: "The FBI said to the world that he was a big terrorist and they have to now say to the world, that this man is innocent.
"They've destroyed his life, his future and his dream."
'No terrorism charges'
The judge said he was allowing bail as the US government was unlikely to bring terrorism charges in the near future.
"Inevitably the investigation is a long and painstaking one and all possible steps must be brought to bring the perpetrators to justice," he said.
Mr Raissi is charged with making a false statement, including failing to declare an old tennis injury, when applying for a pilot's licence from the US Federal Aviation Authority.
The United States prosecution had hoped these would be "holding charges."
James Lewis, for the US Government, told the court Raissi should not be granted bail.
"We are concerned with an investigation into an atrocity that shocked the civilised world", he said.
'Wrong man'
Lawyers for Mr Raissi, who had been in custody for almost five months, said the way he had been treated was a "complete outrage".
Hugo Keith, representing Raissi, said his client would not have been denied bail if he faced the same charges in the UK.
"The Americans now seem unwilling to withdraw from their initial position and accept on this occasion, they pursued the wrong person.
"He is not a fundamentalist. He is married to a white Catholic."
Outside court Mr Raissi's solicitor Richard Egan said his client maintained his innocence about the 11 September atrocities and was confident the remaining charges against him would be dismissed.
Metropolitan Police officers arrested Mr Raissi under the Terrorism Act on 21 September.