Featuring leading performers Aaron Tveit and Karen Olivo singing "Come What May", the number is a bittersweet reflection on the New York show as it remains closed during the pandemic.
The West End transfer of the show is pencilled in for autumn 2021 at the Piccadilly Theatre.
The production also recently received 14 Tony Award nominations, including Best Musical.
Directed by Alex Timbers, Moulin Rouge! has a book by John Logan, choreography by Sonya Tayeh, and music supervision, orchestrations, and arrangements by Justin Levine. The design team includes Derek McLane (sets), Catherine Zuber (costumes), Justin Townsend (lighting), Peter Hylenski (sound), David Brian Brown (wig and hair design), and Sarah Cimino (make-up design). Casting is by Pippa Ailion.
The film version of Moulin Rouge! premiered in 2001, starring Ewan McGregor and Nicole Kidman. It follows a group of bohemian artists trying to gain favour and keep afloat in Montmartre in Paris. At the 74th Academy Awards it was nominated for eight Oscars, winning two.