The national carrier already owns just under 20% of Alliance after it acquired a stake in February 2019 and had expressed interest in owning 100%.
The $4.752 per share deal is backed by the Alliance board but will require shareholder approval and clearance from the Australian Competition and Consumer Commission.
Qantas says the deal will enable it to better serve the resources sector and compete in the highly competitive charter segment.
Alliance has a fleet of 70 jet aircraft that seat up to 100 people each, and accounts for about 2% of the Australian domestic market.
Qantas is Alliance's biggest single customer, with a long-term agreement that sees Alliance operate up to 18 newly acquired E190 jets for QantasLink.
"Alliance's fleet of Fokker aircraft are perfect for efficiently serving resources customers in WA and Queensland," Qantas CEO Alan Joyce said.
"They also have a big inventory of spare parts that would significantly extend the practical life of a combined fleet of around almost 70 Fokkers.
"Keeping these aircraft operating reliably for longer than either carrier could achieve by themselves will help keep costs down, which is ultimately good news for charter customers. There are also benefits from bringing together our operations planning and training facilities.
"The resources sector continues to grow and any new tender for airline services will be very competitive. It makes a lot of sense for us to combine with Alliance to improve the services we can offer, which is a positive for both airlines as well as the travelling public."