The five-match one-day series will run from January 11-23, while the two T20s will be played in Sydney on January 26 and Melbourne on January 28.
The injury-ravaged tourists will welcome back an in-form Malinga after his devastating KFC Twenty20 Big Bash League stint with Melbourne Stars.
Sri Lanka will contest the one-dayers and T20 matches without injured star batsman Kumar Sangakkara (finger) and Chanaka Welegedara (hamstring) who have already been sent home from Australia.
They will also be without wicketkeeper Prasanna Jayawardene (finger) who will miss the Sydney Test.
Sri Lanka squad: Mahela Jayawardene (capt), Angelo Mathews, Tillakaratne Dilshan, Upul Tharanga, Lahiru Thirimanne, Dinesh Chandimal, Lasith Malinga, Nuwan Kulasekara, Thisara Perera, Akila Dananjaya, Ajantha Mendis, Jeevan Mendis, Suranga Lakmal, Rangana Herath, Kushal Perera, Shaminda Eranga.