Kino, translated to 'cinema' in several languages, will be housed in the company's newly-renovated Grade-II listed building in New Briggate.
Opening in July, the restaurant will serve cheese and charcuterie over the summer, as well as a wine list, craft beer and cocktails.
From September, the restaurant will open with a full food menu, as well as hosting guest chefs and residencies with local businesses.
Kino will seat up to 100 people across three floors.
The restaurant’s name and design take inspiration from the history of the site, which was formerly a cinema, with minimalistic decor.
It will work with independent food and drink suppliers, including Leeds’ George & Joseph, North Star Coffee Roasters, Latitude Wines and Northern Monk in addition to Darlington’s Acorn Dairy, Lishman’s of Ilkley and Bluebird Bakery.
To reduce its carbon footprint, the restaurant will run on renewable electricity from both its own solar panels and from the grid.
Kino is part of a £18million programme at Opera North, which includes the transformation of its Howard Assembly Room gig space.
The company's general director Richard Mantle said: "Opening Kino is the final piece in the puzzle following our transformative £18 million redevelopment programme, Music Works.
"Located next to Leeds Grand Theatre, where Opera North is a resident company, and below the Howard Assembly Room, the most eclectic music venue in the north of England, Kino will be the perfect spot to enjoy drinks and a bite to eat before a performance, or as a destination in its own right.
"With Kino, we continue to do what we do best – entertaining through memorable experiences – adding seriously delicious food and drink to our repertoire.”
The assistant manager of George & Joseph cheesemongers, which will supply some of the restaurant's first food, said: “We are very excited at the news of yet another great restaurant opening in our great city.
"We are even more excited and proud to be collaborating with and supplying Kino with a great selection of local artisan cheeses.
"The more places people can enjoy cheese the better in our eyes, roll on July when Kino opens."
Kino will open on July 6 - initially on Wednesday and Thursday evenings, and all day on Fridays and Saturdays.