Mr Mullen will join as chairman-elect on July 1 and take over the top role once Richard Goyder retires before Qantas' annual meeting in October.
The incoming leader will be part of a new management team that includes chief executive Vanessa Hudson, who replaced Alan Joyce last year after the airline faced turbulent times.
Mr Goyder and Mr Joyce attracted plenty of controversy in recent years.
There was a High Court defeat over illegal job outsourcing, allegations the airline sold tickets to cancelled flights, and executive pay increases amid mass redundancies after it weathered the impacts of COVID-19.
Australian and International Pilots Association president Tony Lucas urged Mr Mullen to help Ms Hudson bring about the cultural change she had promised.
"We look forward to greater accountability at the board level for decisions which affect the travelling public and dedicated Qantas staff," he said.
"Mr Mullen, the new board and the Qantas management team owe it to all Australians to restore Qantas to the brand that makes us all proud."
The Transport Workers Union was also optimistic.
It said Mr Mullen had an open-door approach to the concerns of workers while he was chair of transport group Toll Holdings.
National secretary Michael Kaine said the appointment was the first sign Qantas recognised it needed a shift in approach to unionised workers.
"John Mullen has a track record of the earnest determination and openness required to steer the ship back towards the cherished icon Qantas once was," he said.
Qantas is still locked in court battles over compensation with workers who were illegally sacked.
Mr Mullen knows the challenges of large workforces and complex operations.
He was chairman of Telstra for seven years and serves the same role for pallets and containers provider Brambles as well as Treasury Wine Estates.
He will make changes to his roles to accommodate Qantas.
"I am conscious of the time commitment that this prestigious role requires and will be adjusting my other professional obligations to ensure that I can be fully focused on this exciting challenge," he said.
His transport and logistics experience includes roles at DHL, Macquarie Airports and TNT.
In the same announcement, Qantas said Nora Scheinkestel will join the board from March 1 as a non-executive director.
Ms Scheinkestel is on the board of Brambles, Origin Energy and Westpac.
Qantas is due to provide its first-half earnings on Thursday.
