Grant, who was paired with Flavia during last year's Strictly series, will play Argentinian bar owner Carlos in the show, which runs for a strictly limited season at the Phoenix Theatre from 30 January to 2 March 2013.
Producer and former Strictly judge Arlene Phillips said: "Russell's partnership with Flavia is well known, but I too have had a dance partnership with Russell, which began with his appearance in the title role of The Wizard of Oz at the London Palladium, followed by playing Teen Angel in the current national tour of Grease, and I'm delighted we now have a third partnership."
Phillips and co-producer Adam Spiegel also announced today that they are rescheduling press night to tie in with Grant's birthday on 5 February.
Midnight Tango is set in a late-night bar in downtown Buenos Aires. The show, which "brings to life all the drama, sensuality and elegance of the tango", is choreographed by Vincent and Flavia who are joined on stage by a company of ten other tango dancers.
The West End run is followed by a UK tour which kicks off in Eastbourne from 13 to 16 March 2013 and will visit Norwich, Woking, Southend, Bath, Nottingham, Wycombe, Birmingham, Newcastle, Truro, Cardiff, Hull, Northampton, Canterbury, Manchester and Leeds.