The musical was first seen at the Royal Court Theatre in June 1973 and has since been performed in over 20 countries and 10 languages.
It will begin a year-long UK national run, starting on December 20 at Brighton's Theatre Royal.
The play centres around Brad and his fiancée Janet who meet Dr Frank-N-Furter after their cab breaks down.
Christopher Luscombe directs the new run of the production, with the cast yet to be confirmed.
Previous stars in The Rocky Horror Show over the last four decades have included Russell Crowe, Tim Curry, Jerry Springer and Meat Loaf.
It was adapted into cult movie The Rocky Horror Picture Show in 1975. The film is still on limited release, making it the longest-running theatrical release in film history.
Songs in the production include 'Science Fiction/Double Feature', 'Dammit Janet' and 'The Time Warp'.
Tickets for the new run are priced from £12.00 to £29.50 and are available now via ATG Tickets.
Confirmed 2013 dates for The Rocky Horror Show 40th Anniversary Tour are as follows. Further dates will be announced.
- December 20 - January 5 - Brighton: Theatre Royal
- January 14 - January 19 - Bristol: Hippodrome
- January 21 - January 26 - Wimbledon: New Theatre
- January 28 - February 2 - Birmingham: New Alexandra Theatre
- February 4 - February 9 - Aylesbury: Waterside Theatre
- February 11 - February 16 - Liverpool: Empire Theatre
- February 18 - February 23 - Sunderland: Empire Theatre
- February 25 - March 2- Glasgow: King's Theatre
- March 11 - March 16 - Edinburgh: Playhouse Theatre
- March 18 - March 23 - Grimsby: Grimsby Auditorium
- March 25 - March 30 - Manchester: Opera House
- April 8 - April 13 - York: Opera House
- May 6 - May 11 - Richmond: Richmond Theatre
- May 20 - May 25 - Stoke: Regent Theatre
- May 27 - June 1 - Bromley: Churchill Theatre
- June 24 - June 29 - Woking: New Victoria Theatre
- July 8 - July 13 - Torquay: Princess Theatre
- July 15 - July 20 - Milton Keynes: Milton Keynes Theatre
Watch a trailer for a 2010 revival of The Rocky Horror Show below: