As part of the restructure, the Thai restaurant group will exit leases in Oxford Circus, Manchester, St Albans and Reading.
The Alan Yau-founded concept was acquired by London-based buyout specialist Tnui Capital earlier this year.
According to documents filed at Companies House, Tnui Asset Finance Ltd has £21.m of equity in the company, and so has 71% of creditor voting rights.
HMRC, Shaftesbury and the City of London voted against the proposals.
Duff and Phelps, which handled the process, said even when connected parties were excluded, creditors voting in favour exceeded the requisite majority of 50% or more.
The Terry Harrison-led company has nine sites open, with three, in Covent Garden, Leicester Square and the O2 understood to remain closed.
Busaba is the latest in a long line of casual dining chains to restructure its business via a CVA in a bid to mitigate the impact of the Coronavirus crisis.
Earlier this week it emerged that Spanish restaurant group Ibérica is to close two of its seven sites following a CVA, while Revolution Bars Group has launched a CVA that it hopes will see it exit six of its venues.