The restaurant in Leeds was one of four Livebaits which was placed into administration in November last year following the collapse of Paramount. They went on the market along with 18 Brasserie Gerards and three Bertorellis.
After acquiring Livebait Manchester last year, SBG had said they would be looking at cities such as Leeds and London for further expansion of their company.
The 65-cover Leeds restaurant, situated in The Calls area of the city, will remain trading as it is before a relaunch in the spring. All staff, including head chef John Wilkinson and general manager Tom Darlison will remain.
Muir said the company was 'delighted' to take over the fish and seafood restaurant. "Leeds has a really strong food culture and we will bring something a bit different to eating out in the city," he said.
The relaunched restaurant could feature a dedicated Champagne bar and wine menus will be overhauled to 'better reflect what people are drinking' with an emphasis on quality and 'sensible' pricing.
New menus, developed by SBG's executive chef Dave Spanner and Wilkinson, will be introduced to the restaurant over the next few weeks with an emphasis on locally-sourced fresh fish and shellfish while grill dishes and vegetarian options will also feature.
Set up last November, SBG Restaurants is looking to expand further this year, possibly into London. However, it has not yet confirmed if it will buy the remaining two Livebaits in London.
So far, La Tasca, Prezzo, Spaghetti House and Brasserie Blanc have joined SBG Restaurants in taking over former Paramount Restaurant sites. The 25-strong group went into administration in November 2011 after a restructure of the business failed to work.