An invasion of tiny Elsas – and a few Annas – will hit London in autumn 2020, as the stage musical of Disney’s hit film Frozen has been confirmed for the West End.

The show, which features 12 new songs, has been running on Broadway for a year and was nominated for three Tony awards. It will now reopen Andrew Lloyd Webber’s Theatre Royal Drury Lane, a grade I listed Regency building that is undergoing a £45m renovation and restoration project.

Jennifer Lee, who wrote the book for the musical, said: “We’re so humbled by the continued support for Frozen – at its heart, a joyous story about love and sisterhood. We’re very excited to share what we have created on stage with London and to see it come to life in that gorgeous theatre.”

Casting for the production has not yet been announced. It will be directed by Michael Grandage and choreographed by Rob Ashford, with set and costume designs by Christopher Oram.

Jelani Alladin and Andrew Pirozzi in Frozen: The Musical on Broadway. Photograph: Deen van Meer

Kristen Anderson-Lopez and Robert Lopez, the married couple who wrote the music and lyrics, commented: “The power of Frozen comes from the story of two strong, very real women saving their world by leaning in to their deep love for one another. Expanding this story has been an absolute joy. We went deeper and discovered several song moments that enrich the story in a new emotional and theatrical way.”

In her three-star review of the Frozen musical on Broadway, the Guardian’s Alexis Soloski wrote: “With its music, its dance, its flurry of likable leads, and snowball after snowball of son and lumière … it offers most of the pleasures that we count on Broadway musicals to provide.” But she concluded that it “rarely feels like more than the movie and sometimes it feels like less”.

A Frozen sequel opens in UK cinemas this November. The Frozen musical has a North American tour planned for this autumn, and a production is opening in Australia in 2020.