The seven-year deal will see the caterer manage and develop all aspects of the catering and hospitality services at the theatre's Vaults restaurant, theatre bars, and the 1805 Rooms, which are used for functions.
It is the latest in a series of contract wins for the new division created just a year ago by the Lindley Group to expand its business into heritage and arts & leisure venues.
According to Caterer and Hotelkeeper, other key wins include a £4m five-year contract extension at Malvern Theatres in the West Midlands and a five-year deal at Yorkshire art gallery Hepworth Wakefield, worth £1.8m.
Danny Moar, director at the Theatre Royal Bath, said: "We've been very impressed with Lindley Heritage's success in developing the Scene Bistro at the Malvern Theatres, and the knowledge they have of business in the local area through managing the catering at Bath Racecourse and at Bristol City FC's Ashton Gate Stadium."
Adam Elliot, Lindley Group chief executive, added: "Theatre Bath Royal is one of the country's premier regional theatres and with its prime city centre location it attracts high numbers of theatregoers who make good use of the restaurants and bars so the venue does enjoy a steady income from its catering facilities.
"However, there's huge potential to increase revenue from catering and events outside the theatre's primary business, while building on the thriving pre-theatre dining offering
"Opening the Vaults restaurant for lunchtime business, and proactively marketing the conference and banqueting facilities to members of the public and event organisers as a stylish unique venue, will both play key roles in establishing the theatre as a magnate for diners and anyone looking for a location to serve as a fabulous back-drop for conferences and special occasions."
The emphasis at the Bath theatre will be on quality, fresh seasonal produce sourced locally, while the bars will feature beers from Bath Ales. In due course, the caterer aims to create bespoke "Signature" dishes for the Vaults restaurant.