The change, which will come into effect in time for the next council elections in 2012, has long been supported by Greens councillor Peter Olive.
"I think it's really important to have Aboriginal names and parts of Aboriginal language exposed as much as possible to ensure they remain part of our culture and also as a historical record," he said.
In choosing the names, the council worked with members from the Marrickville Aboriginal Consultative Committee.
The original residents of Marrickville are the Cadigal people, who have lived in the area for more than 40,000 years.
The Cadigal are a clan of the Darug people, whose traditional tongue is the Eora language.
Wirraga, wali, magura and burraga were chosen because they reflected local fauna associated with the areas - such as bandicoots in Dulwich Hill and fish in the Cooks River.
Other criteria included cultural significance and whether they were relatively easy to pronounce. * Source: Marrickville Council
NEW WARD NAMES
* Central Ward: Wirraga goanna
* North Ward: Wali possum
* South Ward: Magura fish
* West Ward: Burraga long-nosed bandicoot