The Menier Chocolate Factory's production of Forbidden Broadway will transfer to the West End's Vaudeville Theatre for a limited 11-week run from 9 September.
Bianco, whose latest YouTube video of "Let It Go" has received over 5 million views, has appeared in Forbidden Broadway: Goes to Rehab in New York.
Forbidden Broadway offers an alternative take on some of the biggest productions from Broadway and the West End, including The Book of Mormon, Charlie and the Chocolate Factory, Once, Matilda, Wicked and Miss Saigon.
Menier artistic director David Babani said: "I can't think of a more fitting way to celebrate our 10th anniversary year than to transfer our wonderful production to the Vaudeville Theatre in the West End so that many more people will get to the opportunity to enjoy it!"
The West End run of Forbidden Broadway will mean a postponement for the previously announced Rabbit Hole starring Joanne Froggatt, which was due to open on 11 September. The producers of the play have said that they "remain committed" to bring the production to London.