The court of appeal in London ordered the government to reconsider the compensation claim on Thursday.
It said that the way extradition proceedings and refusals of bail had been conducted were "an abuse of process".
The US had argued that Raissi was linked to Hani Hanjour, the pilot suspected of crashing a passenger plane into the Pentagon in Washington.
It had sought to extradite Raissi on two counts of falsifying an application for a US pilot's licence, but a British court dismissed the charges in 2002.
After the appeal court ruling, Raissi said he wanted a public apology from the British government.
He said: "I want a widely publicised apology for the part that they played. I am not a terrorist, I abhor terrorism."
Britain's ministry of justice said it was considering whether to appeal against the ruling.