Reeves will explore how Dada helped shape 20th Century culture with the help of Armando Iannucci, Terry Gilliam and Arthur Smith.
Turner Prize winner Martin Creed will also contribute to Gaga for Dada: The Original Art Rebels.
Reeves, whose real name is Jim Moir, said: "It was the Dadaists who proved the most important (artists)."
Reeves and his team will restage an early Dada performance in Zurich's Cabaret Voltaire, where the movement first began.
Dada, according to the Tate, was "an art movement formed during World War One in reaction to the horrors and folly of the war", adding that the art, poetry and performance produced "is often satirical and nonsensical in nature".
Other programmes that are part of the season include Who's Afraid of Conceptual Art? which explores the suspicion and scepticism often surrounding the movement.
There will also be a one-hour special about the eccentric British artist Bob Parks, who was known for his outrageous performances, and a documentary coinciding with the 40th anniversary of the infamous Tate Bricks.
In 1976, the exhibition of Carl Andre's 120 fire bricks laid out on the floor of the Tate Gallery caused huge controversy.
The documentary will examine whether Andre's artwork paved the way for a greater appetite for conceptual art.
Cassian Harrison, channel editor for BBC Four, said: "Bold, baffling, witty and adventurous - there's a lot that BBC Four and conceptual art could be said to have in common - so I'm delighted to celebrate this most uncompromising of art movements with a major season on BBC Four."
The programmes will all fall under the umbrella title, BBC Four Goes Conceptual, following on from the success of last year's BBC Four Goes Pop and 2014's BBC Four Goes Abstract.
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Comedian Vic Reeves is to recreate a Dada performance as part of a new BBC Four art season.