In Extremely Wicked, Shockingly Evil and Vile, Bundy's story will be told from the view of his girlfriend.
Elizabeth Kloepfer couldn't believe Bundy had murdered more than 30 women in the 1970s but finally turned him in.
Efron's gear change my surprise his fans - but they can catch him next in the film remake of TV hit Baywatch.
Extremely Wicked, Shockingly Evil and Vile will see Efron play Bundy as a figure of evil but who is seemingly quite ordinary - even charismatic.
It's being made by the Oscar-nominated Joe Berlinger, who previously made a documentary about the West Memphis Three, young men who were convicted and sent to prison for the 1993 murders of three boys but who later had their convictions overturned.
Berlinger also made a documentary about the heavy metal band Metallica called Some Kind of Monster.
Efron will start work on the Bundy film in October having recently completed The Greatest Showman.
That movie is about the legendary 19th Century American circus founder PT Barnum, who is being played by Hugh Jackman.
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Zac Efron - the star of the High School Musical films and comedy Dirty Grandpa - is changing course by signing up to play the US serial killer Ted Bundy.