EARLIER: United Airlines passengers endure the day from hell
The departures cap a tumultuous week for the airline with a return to profit announcement overshadowed by a series of technical faults with aircraft.
CEO Alan Joyce will remain in place, overseeing a more streamlined executive team.
In a statement issued to the Australian Securities Exchange, Mr Joyce recognised the contribution made by Mr Hickey and Mr Strambi.
Lyell and Simon have helped build a stronger Qantas, said Mr Joyce.
I would like to thank them for their tremendous contribution and wish them well for the future.
In Mr Hickeys ten years at Qantas, he held various senior roles including CEO of Qantas Frequent Flyer, moving over to the troubled international arm in May 2012.
Mr Strambi served the airline for six years, most recently as the head of Qantas Domestic which recorded a $335 million decrease in profits last financial year.
Mr Joyce said the business had faced a tough market environment but had risen above the competition to emerge as a stronger and leaner business.
But there is still a lot of work to build the foundation for a stronger, more sustainable and more successful Qantas, he said.
This new executive team will lead this work forward to deliver for our customers, shareholders and employees according to the strategy we have laid out.
Mr Hickey said he felt privileged to have worked with a dedicated and passionate team of people at Qantas but now was the right time to explore new opportunities.
Mr Strambi also said the time was right for him to look for new challenges outside the aviation industry.
Im proud of the progress made and have no doubt Qantas can keep improving into the future, ensuring the airline remains this countrys first choice for business travellers, Mr Strambi said.
Other changes announced include the axing of the position of QantasLink CEO.
John Gissing will instead become group executive for associated airlines and services, including QantasLink, Network Aviation and Jetconnect.
Group Chief Financial Officer Gareth Evans will take over as Qantas International and Freight boss and Chief Operating Officer Andrew David will move into Mr Strambis office as head of Qantas Domestic.
The executive restructure will begin to take effect from the new year.