Qantas will also sell its 50 percent stake in freight and logistics business StarTrack to Australia Post, receiving net proceeds of A$408 million ($422 million).
Under joint venture arrangements since 2003, Qantas and Australia Post each currently owns 50 percent of Australian Air Express and StarTrack.
Qantas Group Chief Executive Alan Joyce said the acquisition of Australian Air Express would boost a core business area.
"We will be able to offer an integrated air freight product across domestic and international networks," Joyce said in a statement on Tuesday.
Qantas has been stripping costs out of its business after a year troubled by a record fuel bill, rising competition and a labour union that has opposed the carrier's spending cuts.
In August, it cancelled orders for 35 Boeing Dreamliner jets to further cut costs after posting its first net loss in 17 years. (Reuters)