The centre has received planning consent for the development and bosses are currently in discussions with two well-known cinema brands.
Work on the £8 million investment will begin later this year, ahead of a spring 2020 opening.
It comes just a day after a separate, new £8.5 million cinema and restaurant complex was announced for Sir Nigel Gresley Square.
The planning permission is part of an ongoing investment strategy by the centre’s owners, The Frenchgate Limited Partnership.
Occupying 15,000 sq ft and comprising up to eight screens, depending on configuration, the cinema will be complemented by a further proposed development of three new food and drink operators totalling in excess of 6,000 sq ft.
The cinema space will occupy the remaining part of the former BHS on North Mall, which is also home to a 30,000 sq ft Flip Out trampoline park.
Frenchgate was the first shopping centre in the UK to achieve a change of use from retail to leisure for a former BHS. The proposed restaurants will be created within existing adjacent space.
The cinema and supporting food offer will be directly accessed from the mall of the existing busy centre, which has an annual footfall of 16 million.
The new offer will join a strong line-up of retail and leisure brands, with Flip Out, Lovisa and Taco Bell all opening at Frenchgate in the last 12 months.
In addition, Dunkin’ Donuts and Ramsden’s will open in the coming weeks, and Greggs is due to upsize on ‘Eat Street’ at Frenchgate.
Commenting on the news on behalf of The Frenchgate Limited Partnership, Paul Devlin said: “The new cinema will be an exciting addition to Frenchgate, expanding on our adventurous leisure offer and evolving a retail destination that reflects the changing needs of contemporary consumers.
“Situated in such a central location, we are the hub of the town, providing visitors from across the region with an experience for everyone to enjoy.”
Meanwhile, it was announced yesterday that work is set to start on another new £8.5 million cinema and restaurant comple in Doncaster.
The complex will be next door to the Cast performance venue in the Cultural and Civic Quarter.
Doncaster Council has appointed Lindum Construction Limited to build the development and has now signed an agreement with cinema operator Savoy.
Construction is due to commence in May.