Running in the Crucible from 8 December 2013 to 17 January 2014 (previews from 28 November), the production features choreography by Alistair David and is produced in association with Stage Entertainment.
Anything Goes features classic numbers including "I Get A Kick Out of You", "You're the Top", "It's De-Lovely" and the title song, and promises "tap dancing sailors, sassy heroines and a thrilling Christmas treat". Casting is still to be announced.
Evans' previous musical productions for Sheffield include Oliver!, My Fair Lady and Tim Firth's award-winning This is My Family, which is returning for a run in the Lyceum in October.
As previously announced, the 2014 will also see associate director Richard Wilson making his Sheffield stage debut in Beckett's Krapp's Last Tape (25 June-19 July, Studio), directed by Polly Findlay. And Jonathan Watkins' dance-theatre adaptation of Barry Hines' novel Kes runs in the Crucible from 27 March to 5 April as part of the Yorkshire Festival.
The season also features a second collaboration with English Touring Theatre, Twelfth Night, which sees Jonathan Munby return to Sheffield Theatres to direct.
Other productions include, as previously reported, Jonathan Humphreys' revival of Marc Camoletti's farce Boeing Boeing (15 May-7 June), about a man juggling three girlfriends. And the Crucible will also host Chris Bush's The Sheffield Mysteries (15-19 July), also directed by Evans, which is inspired by and responding to the medieval mystery cycles.
"I'm delighted to announce our autumn season," Evans said today, "particularly as it combines two strands of work of which we are incredibly proud: classical theatre and musical theatre."
He added: "I'm especially pleased that we are able to remount Tim Firth's This Is My Family in the Lyceum after its award-winning run in the Studio last year. It's also a mark of the company's confidence that there will be two productions touring the country: Twelfth Night (with ETT) and This Is My Family. It's wonderful to be able to take the work we make in Sheffield to a wider audience across the UK."