As a result of the deal, 216 members of Prezzo's 2,900-strong team have been made redundant.
The group's remaining 156 restaurants are expected to reopen once Coronavirus lockdown restrictions are lifted.
It was reported earlier this week that Cain, which bought Prezzo's debt and equity back in December, was in discussions with scores of landlords about future rent arrangements and the payment of arrears, and exploring whether to put the chain through an insolvency process.
Jonathan Goldstein, chief executive of Cain International, said: “We firmly believe that strong hospitality businesses, such as Prezzo, have a bright future and will play an essential role in reviving the UK economy. However, to do so we must get through this current crisis of mounting liabilities and no revenues.
“The lack of visibility on when and how the sector will reopen has heightened economic uncertainty to the point where decisive action had to be taken to secure the future of the business and the majority of jobs for Prezzo's people.
"We are deeply sorry for all those affected by the permanent closure of the 22 non-viable restaurants.
"It was a difficult but essential decision to take but doing so will allow us to save thousands of jobs and create more in the future.”
Prezzo will continue to be led by its existing management team, which is run by executive chair Karen Jones.