Presented by Ambassador Theatre Group, the tour kicks off at Manchester Opera House on 12 May and will subsequently visit venues including Edinburgh, Birmingham, Bromley, Liverpool, Glasgow and Wimbledon (full tour schedule below).
Williams, whose West End credits include Love Story and Chitty Chitty Bang Bang, will play the title role of sharp-shooting country girl Annie Oakley, who falls for the chauvinistic marksman Frank Butler (Donovan) at a contest run by Buffalo Bill (Pace).
Jason Donovan, whose West End credits include Joseph and the Amazing Technicolor Dreamcoat and Priscilla Queen of the Desert, said: "I've been very lucky in having some great roles to get my teeth into in the past... I'm very much looking forward to performing such brilliant songs and appearing alongside a truly great cast as we bring the Wild West to theatres across the country."
Former Regent's Park Open Air artistic director Ian Talbot will helm the production.
Irving Berlin's score for Annie Get Your Gun includes classics "There's No Business Like Show Business", "Doin' What Comes Natur'lly" and "Anything You Can Do I Can Do Better".
Full 2014 tour dates:
12 – 13 and 19 – 24 May - Manchester Opera House
3 – 7 June - Sunderland Empire
10 – 14 June - Stoke Regent Theatre
17 – 21 June - Edinburgh Playhouse
24 – 28 June - Oxford New Theatre
1 July – 5 July - Birmingham Alexandra New Theatre
15 – 19 July - Churchill Theatre, Bromley
22 – 26 July - Aylesbury Waterside Theatre
29 July – 2 August - Malvern Festival Theatre
5 August – 9 August - Liverpool Empire
12 August – 16 August - New Victoria Theatre, Woking
19 August – 23 August - Bournemouth Pavillion Theatre
26 August – 30 August - Brighton Theatre Royal
2 September – 6 September - Glasgow Theatre Royal
9 September – 13 September - Wimbledon New Theatre
16 September – 20 September - His Majesty's Theatre, Aberdeen
30 September – 4 October - Torquay Princess Theatre