The British production previously won both an Olivier and a WhatsOnStage award for best new musical.
Operation Mincemeat first played in London at the 80-seater New Diorama Theatre, a charming but modest venue which provides a home for independent theatre.
After further development runs at London Fringe theatres, the show transferred to the Fortune Theatre.
Despite being one of the West End's smaller theatres, it attracted a dedicated cult following, including a group of fans who call themselves "Mincefluencers".
The re-worked version attracted positive reviews from critics, with many awarding four or five stars.
The Telegraph's Marianka Swain described it as a "glorious combination of ingenious, silly and surprisingly moving".
"It honours these war heroes, but with that key British asset: a sense of humour," she added.
"They're laser-focussed on getting us to laugh," noted Time Out's Andrzej Lukowski. "There's little of the saccharine baggage of the average musical, no romance, no learning life lessons, no big introspective moments."
The Evening Standard's Nick Curtis said it was an "exuberant, energetic, incurably daft show", adding its "five-year journey through fringe and regional theatres has become part of the story".
