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The veteran actor will play the curator of a Vincent van Gogh exhibition in the episode, which is penned by Richard Curtis.
A set insider told DS: "It was a real coup to get Bill Nighy in Doctor Who, especially in Richard Curtis's amazing episode. Bill plays a van Gogh expert with some similar fashion choices to The Doctor himself."
The story is set both in the present day and 19th Century France. This Life actor Tony Curran was previously confirmed in the role of van Gogh.
The episode - the tenth in the new series - was filmed on location in Croatia and Cardiff over Christmas.
A BBC spokesperson said: "We do not comment on storyline or character speculation."
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