Sky News reports that the deal with GBK's current owner, the South Africa-based Famous Brands, is expected to take place later this week.
The deal is expected to save roughly 650 jobs and 35 of GBK's restaurants, meaning that dozens more are likely to close permanently with the loss of several hundred jobs.
Prior to the pandemic, GBK UK operated from 62 restaurants and employed nearly 1,300 staff.
Boparan Restaurants is understood to have seen off competition from the new owners of GBK's rival burger chain Byron, investment firm Calveton UK, to clinch a deal.
Owned by Ranjit Singh Boparan, Boparan has a history of snapping up troubled restaurant business.
In May the group acquired ailing restaurant chain Carluccio's in a deal worth just £3.4m.
GBK was founded in Battersea, London in 2001 by three New Zealanders with the backing of chef Peter Gordon.
It was bought by investment firm Yellowwoods Group in 2010, leading to rapid growth of the chain; and was then subsequently acquired by Famous Brands in 2016, which led to a further period of expansion focused on regional locations outside of the chain's London heartland.
The chain eventually underwent a financial restructuring in 2018 in the form of a Company Voluntary Arrangement (CVA), which resulted in the closure of dozens of restaurants.