The consortium, called Creative Broadcast Services, consists of investment fund Macquarie Capital Alliance Group and Macquarie Bank Limited, Australia's largest investment bank.
Apax Partners, where former director-general Greg Dyke is an adviser, French technology company Thomson/Technicolor and finance firm Exponent Private Equity were cut from the running.
John Smith, BBC chief operating officer, said it choose Creative Broadcast Services because the company would be the best partner and would expand the company giving the best possible opportunities for BBC staff.
"Creative Broadcast Services made the BBC a great offer and showed real capabilities in managing a contractual long-term partnership with a commitment to growing and investing in the business," he said.
Unions had been concerned that the deal would lead to redundancies, but a spokeswoman for Macquarie Capital Alliance said that there was no plan for "any staff redundancies during the one-year moratorium".
"Our focus is on growing the business," she said.
The sale is subject to the final approval of the secretary of state for culture, media and sport Tessa Jowell, with the handover expected in summer.
The business was put up for sale as a result of internal reviews by BBC director-general Mark Thompson on how to make the BBC more accountable to its licence-fee payers.
As well as axing 3,750 staff over three years and moving a further 1,500 jobs north to Manchester, Thompson warned the BBC's commercial operations would be reviewed and potentially put up for sale as part of the £320m cost-saving initiatives.
BBC Broadcast offers a range of media services to the BBC including transmission, outside broadcast, mobile services and promotional services such as creating new idents.
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