The corporation said the story is “firmly in the public interest” and will run in the coming days.
The BBC alleges that the man, known in court proceedings as X, is a covert human intelligence source (Chis) for MI5, who physically and psychologically abused two female partners.
This ruling enables us to tell a story we believe is firmly in the public interest, and it is a vindication of the BBC’s investigative journalism
An injunction remains in place to prevent the BBC from disclosing information likely to identify X.
Attorney General Suella Braverman sought an injunction to block a planned broadcast which would identify the man, arguing it would damage national security and create “a real and immediate risk of serious or life-threatening harm” to him.
Mr Justice Chamberlain has previously said the BBC can still air the programme and the key issues, but not identify X.
Lawyers representing Ms Braverman said at a previous hearing that she “neither confirms or denies” the BBC’s claim that X is an agent, but conducted the case on the “hypothetical assumption” that he is or was.
Following the publication of a ruling on Wednesday, the BBC said: “This ruling enables us to tell a story we believe is firmly in the public interest, and it is a vindication of the BBC’s investigative journalism.”