​Australia's second-largest airline has been searching for a new chairman since Mr Chatfield declared his intention in October to relinquish the reins after seven years in the role.

Virgin said Ms Bryan, who is also a director of Insurance Australia Group, had a proven track record as a successful chairman in diverse industries in which she had overseen significant change.

Her selection as chairman comes ahead of the release on Friday of Virgin's quarterly earnings results, which are expected to show the airline continuing to benefit from the end to a capacity war with Qantas in the domestic market and oil prices hovering near $US60 a barrel.

Virgin has to provide quarterly earnings because one of its three major shareholders, Singapore Airlines, releases its figures every three months and accounts for its interest in the airline in its own results.

Ms Bryan's previous roles include chief executive of Deutsche Asset Management Australia and chairman of UniSuper.

"Virgin Australia has transformed the aviation industry in Australia and I look forward to working with the board to continue to grow the business," Ms Bryan said.

However, Australian Shareholders Association chairman Ian Curry said he had concerns about Ms Bryan's greater workload once she began in the role at Virgin, given her existing board commitments at Caltex, Westpac and IAG.

"We would have concerns, not about her ability to be a good director or chairman, but the time available to manage all of those very different businesses," he said.

"The businesses that she is in – Caltex and Virgin – are facing challenges."

Ms Bryan's selection was a surprise to investors given Virgin had a strong line-up of potential internal candidates, including former trade minister and board director Mark Vaile.

Former finance minister Lindsay Tanner and high-profile businessmen Graham Bradley and Tony Shepherd also sit on the board of the holding company overseeing Virgin's international operations.

Ms Bryan will take the reins from Mr Chatfield on May 20.

Mr Chatfield, who has had a relatively low public profile at the airline, was appointed as a Virgin director in May 2006. Just over a year later, he was appointed chairman.

One of his most significant decisions was to appoint John Borghetti​, a former Qantas executive, as Virgin's chief executive in 2010.

"Elizabeth is an ideal replacement as chairman and I have full confidence that the skills and extensive experience she brings to the board will take the business to even greater heights," Mr Chatfield said.

Virgin independent director Sam Mostyn led a committee to run the selection process for a new chairman.

Over the past few years, Air New Zealand, Etihad and Singapore Airlines have emerged with a combined stake of about 70 per cent in Virgin. Sir Richard Branson's Virgin Group also has a 10 per cent stake.

The possibility of tension arising on the board from its three largest shareholders each holding a directorship has been one of the biggest concerns for investors.

Shares in Virgin have risen 38 per cent over the past year, closing unchanged at 52.5¢ on Tuesday.

However, the stock's appreciation has been overshadowed by Qantas, which has soared by 176 per cent to $3.30 over the same period.

Morgans analyst Mark Williams said Virgin stood to benefit from the same favourable industry dynamics as Qantas after a period of significant losses.

"However, Virgin still needs to prove its evolving strategy can deliver sustainable earnings growth over the long term," he said.

"Gradual gains in the higher yielding corporate market should continue to yield mix benefits, although the key for Virgin will be restraining unit-cost growth below yield growth."

Despite the improved outlook, Mr Williams said Virgin remained more vulnerable than Qantas to industry shocks because of a higher debt burden and its limited liquidity would act as a restraint on share price gains.