Plans to close 27 Giraffe and Ed's Easy Diner restaurants have been approved by creditors, putting hundreds of jobs at risk.
The brands will enter a company voluntary arrangement (CVA) and close almost a third of their 87 restaurants.
The business, owned by Boparan Restaurant Group (BRG), first put forward the plan earlier this month.
BRG said sales had improved since the chains were acquired in 2016, but several sites remained unprofitable.
The deal will also give the chains rent reductions at 13 sites.
Will Wright, restructuring partner at KPMG and joint supervisor of the CVA, said: "This is a critical step forward for the business, allowing Giraffe Concepts to complete its financial restructuring plan and embark on a comprehensive operational transformation programme."
Paul Berkovi, director at KPMG, added: "Today's vote saw a significant majority of all voting creditors choosing to approve the CVA, surpassing the 75% total required in order to pass the resolution."
BRG snapped up Giraffe from Tesco in 2016, before combining it with Ed's Easy Diner, which it had bought in a pre-pack administration the same year.
The two brands form a combined entity, which in the most recently available accounts had annual turnover of £67.1m with underlying losses of £1.6m.
The company owns 70 branches of the two chains, with 17 franchised restaurants unaffected by the CVA.
BRG also owns other brands, which are not involved in the CVA. These include fish and chip restaurant Harry Ramsden and the upmarket Cinnamon Collection.
It is also the master franchisee for US brand Slim Chickens, which first opened in the UK last year.
BRG is owned by "chicken king" Ranjit Boparan, who also owns the 2 Sister group, which supplies food to supermarkets such as Aldi, Asda, Co-op, KFC, Lidl, Marks & Spencer, Morrisons, Sainsbury's, Tesco and Waitrose.
Last year, rising costs and tougher competition led to several restaurant brands shutting branches, including Prezzo, Jamie's Italian, Byron, Carluccio's, Gaucho and Gourmet Burger Kitchen.