Virgin Australia has been given the go ahead to sell a 35 per cent stake in its Velocity loyalty program.

The Foreign Investment Review Board has cleared the $356 million sale of the Velocity stake to private equity firm Affinity Equity Partners.

The sale values the Velocity program at $960 million.

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Virgin on Thursday welcomed the decision and said it expected the sale to be completed by the end of October.

The airline announced the sale in early September and expects the move to improve its cash balance by $336 million.

Rival Qantas has refused to sell off part of its $2.5 billion frequent flyer program, despite the airline posting a net loss of $2.8 billion for the 2013/14 financial year.