Administrators Tenon Recovery closed 37 loss-making sites after being called in on November 1, with around 250 job losses.
The Solihull-based chain, which had 158 shops, said it appointed administrators because of a downturn on the high street.
Chairman Geoff Peppiatt told British Baker Tenon accepted an offer from a team, which he is leading, to take over most of the former estate on November 3.
A new chain, Cooks The Bakery, is to be formed out of 121 of the shops, saving 900 jobs.
Details of the deal were being finalised, Peppiatt said. However, the new company has bought some of the intellectual property of Three Cooks, and will continue to refit shops. Three Cooks had been in the process of rolling out a new "Cooks" fascia and refitting stores when it went bust.
The demise of Three Cooks will leave many bakery suppliers exposed as it bought in all its ranges and baked-off in-store rather than having its own bakeries.
Software solutions supplier Alphameric has already written off £1m in the aftermath of the news. Allied Bakeries is also believed to be a supplier.
Three Cooks was owned by RHM until 2003, when it sold non-core businesses. At that time the century-old chain had 250 stores.
Analyst David Lang from Investec said: "The freeholds were sold by RHM before it sold off the chain. The new company was facing rising high street rents and changing eating patterns. It was seriously under the kosh."
Joint administrators Trevor Binyon and Steve Parker said they were delighted to save 900 jobs.