The actress will read Robin’s Winter Song by Suzanne Barton on the BBC channel for pre-school age children.
The heartfelt tale tells the story of a little robin’s first winter.
Menzel, 48, is best known for her role as Elsa in Disney’s Frozen films – the second of which will be in UK cinemas from Friday – and for her Broadway career in hit musicals including Rent and Wicked.
The US star follows in the footsteps of fellow big names such as Sir Elton John, Dolly Parton, David Hasselhoff, Mark Ronson and Tom Hardy in signing up for the star-studded TV slot.
Menzel’s role in settling down young viewers before bedtime comes after it was announced that US jazz singer Gregory Porter will become the first celebrity to sing a CBeebies Bedtime Story rather than read it.
Porter will sing Moon River, the classic ballad from the 1961 film Breakfast At Tiffany’s, on this Friday (November 22)
The original Frozen film - which features the voices of Idina, Kristen Bell and Jonathan Groff – won critical acclaim following its release in 2013.
It later scooped several accolades, including Best Animated Feature and Best Original Song for Let It Go at the Oscars, and Best Animated Film at the Baftas and the Golden Globes.
A stage version of the film has already proven to be a hit on Broadway and will open at the Theatre Royal Drury Lane in London in 2020.
Menzel’s episode will air on Sunday, November 24. CBeebies Bedtime Stories airs daily at 6.50pm.
Additional reporting from Press Association.