Babar Ahmad, who grew up in Tooting, has spent seven years behind bars but the Government did not want the BBC to film and broadcast its interview with the 37-year-old British Muslim.
The broadcasting company took the battle to the High Court where two judges allowed the broadcast saying Mr Ahmad’s case, having been jailed longer than any other British national in modern history without trial, was “highly exceptional”.
The Government has indicated it will not look to appeal the decision and instead will enter talks about the logistics of the interview.
Mr Ahmad is being held under extradition laws as he fights his removal to the United States, where he is wanted for allegedly raising funds for Chechen and Afghan insurgents over the internet.
He strongly denies any involvement with terrorism.
The IT worker is currently held at Long Lartin Prison in Worcesteshire while his extradition case is being decided on by the European Court of Human Rights.
The High Court was told that a ruling was being prepared “as a matter of urgency”.