The London-based burger chain appointed Valentine & Co to supervise the process, with the CVA approved on 11 September, according to documents filed at Companies House.
A majority of 84.3% creditors voted in favour, with 15.6% against, after some modifications were made.
A CVA allows an insolvent company to continue trading and pay creditors over a fixed period.
Patty & Bun Ltd owes creditors £1.7m, with HMRC owed £1.4m, and Shaftsbury £28,000. Shaftsbury proposed that the CVA not apply to the lease of Kingly Street, Carnaby.
Creditors who voted against the proposals include Broadgate Estates, which is owed £267k.
The arrangement involves the repayment of 71p in the pound to all unsecured, non-preferential creditors.
CW Wood Wharf proposed modifications for Water Street, Canary Wharf, with £105k per anum, turnover rent payable in addition to compromised rent. CW Wood Wharf (D1/D2 Limited Partnership), part of Canary Wharf Group, had liabilities of £1.2m, though this was valued at £1 for the purposes of voting, as it relates to future rent and service charges which are unliquidated debts.
According to its website, the Joe Grossmann-led brand has nine sites trading, with two concessions with Swingers.
Earlier this year, Patty & Bun closed its restaurant in Portobello Road, Notting Hill.