Some 91% of creditors approved the Company Voluntary Agreement (CVA), which allows the business to reduce rents while negotiating with landlords.
It is thought around 30 restaurants could close, putting 500 jobs at risk.
The Italian food business, founded by the late Antonio Carluccio in 1999, said it would try to minimise job losses and was relocating staff to remaining outlets where possible.
Mark Jones, chief executive of Carluccio’s, said: “I would like to thank our landlords for their support.
“We now look forward to a positive future and the on-going development of the Carluccio’s business and of course our passionate people.”
Carluccio’s is owned by Dubai-based Landmark Group, which bought it for £90m eight years ago and will invest a further £10m in the coming months.
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Will Wright, restructuring partner at KPMG and joint supervisor of the CVA, said: “This is an important step forward for the business, allowing Carluccio’s to complete its financial restructuring plan and embark on a comprehensive operational transformation programme.”
Other restaurants that have undertaken CVAs this year include Byron, Prezzo and Jamie’s Italian and several retailers, including House of Fraser, have also been caught up in the high street turmoil.