The episode, to air 24 April, will mark Jeremy's first appearance on BBC since being fired from Top Gear last month.
A rep for the corporation said: "Jeremy's contract has not been renewed on Top Gear but he isn't banned from appearing on the BBC."
Jeremy was dropped from Top Gear on 25 March, following his suspension for being involved in a fracas with a producer on the show.
In a lengthy statement explaining the decision, BBC Director-General Tony Hall said: "A member of staff – who is a completely innocent party – took himself to Accident and Emergency after a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature. For me a line has been crossed.
"There cannot be one rule for one and one rule for another dictated by either rank, or public relations and commercial considerations. This decision should in no way detract from the extraordinary contribution that Jeremy Clarkson has made to the BBC."
After the incident, it was confirmed that North Yorkshire Police would begin an investigation, but the force announced this week that no further action would be taken.
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