The corporation wants to air the chat with Babar Ahmad, who is suspected of helping to raise funds for terror groups, from behind bars.
Ahmad is fighting extradition to the US, where he is wanted in connection with terrorism related charges, and has been in detention for more than seven years.
Kenneth Clarke, the Justice Secretary, had refused the interview in accordance with a general policy of not allowing interviews with detainees or inmates to be broadcast.
In a legal first, the BBC challenged that decision and the High Court yesterday ruled the refusal was unlawful and a breach of the right to freedom of expression.
The judges stressed the decision was because of Ahmad’s “highly exceptional” circumstances and did not set a precedent for others.
The Ministry of Justice is not appealing the decision which means the interview will now go ahead.
Ahmad has been detained without trial for longer than any other British national in modern history.
The 37 year-old British Muslim is being held under controversial extradition laws as he fights removal to the US, where he is wanted for allegedly raising funds for Chechen and Afghan insurgents over the internet.
He strongly denies any involvement with terrorism.
Lawyers for Mr Clarke had argued there were compelling reasons for refusing the BBC request having regard to the extreme seriousness of the crimes of which Ahmad stood accused.
But in their judgment, Lord Justice Hooper and Mr Justice Singh, sitting at the High Court in London, said Ahmad’s circumstances were highly exceptional and “justifies departure from the normal policy”.
They stressed the Government was entitled to maintain its policy in other cases.
Ashfaq Ahmad, the detainee’s father, said outside the court: “I urge Mr Clarke to listen to the public and not to appeal this decision. After all, what has the Government to fear from what Babar has to say?”
A Ministry of Justice spokesman said the Justice Secretary accepted today’s judgment – but condemned the “unacceptable” length of time it was taking for the European Court of Human Rights decision on the Ahmad extradition.