The popular party spot's new premises will be located in the former Ricci's Tapas unit on Infirmary Street in the financial district, and will open in autumn 2018.
Arc also operates brands Banyan, The Pit, Manahatta and Kith & Kin in Leeds, Harrogate and York.
The company has invested Â£1.3million in The Box, which will have over 50 staff, seating for 150 customers and 8,000-sq.ft of space.
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It will have large screens for showing sport and serve Mexican street food.
Arc's CEO Martin Wolstencroft said:
“We are thrilled to announce the evolution of our long-standing and most successful concept, The Box. Looking to Leeds city centre for the second location, we’ve taken the elements our customers love about what we do and worked to broaden its appeal, beyond a place as a firm favourite for students, to an inner-city local for day and nights out, for residents, workers and visitors to the city. We’ll feature an amazing range of craft beers and cocktails, accompanied by authentic Mexican street food, experiential games and live sport screens. A unique screening and tap room will provide a great space for private gatherings or corporate events.”
The expansion has been secured by new property director Nik Lowery, who joined the business in February and made the new site his first acquisition.