Under the plan, existing shareholders will contribute £600 million ($750.6 million), including £200 million ($250 million) from Virgin Group, founded by billionaire Branson.
US hedge fund Davidson Kempner is providing an additional £150 million ($188 million) in secured financing and creditors have agreed to defer repayments worth £450 million ($562.5 million).
"Few could have predicted the scale of the Covid-19 crisis we have witnessed and undoubtedly, the last six months have been the toughest we have faced in our 36-year history," Virgin Atlantic CEO Shai Weiss said in a statement.
"We have taken painful measures, but we have accomplished what many thought impossible," he added.