The show, aimed at a high-brow audience, will debut at 10pm coming Friday.
Following the ban, the Corporation has been accused of having a "total sense of humour failure".
However, BBC News said that co-operating with the light-hearted entertainment programme might undermine its journalism reputation.
The show will feature three comedians being cut off from the news for several days in a country house with no access to any media. Then they will be asked to distinguish between authentic and fake news items.
Frank Skinner, American comedian Reginald D Hunter and Victoria Coren will participate in the first episode.
ITV and Sky News have shown interest in the show and agreed to supply it with news footage. BBC has agreed to provide it with archived material.
The show is made by Hat Trick Productions.