The 44 year-old actor and three-time Australian Film Institute award winner was found in a park in Fremantle on Sunday and was pronounced dead at Fremantle Hospital.
Police say they are waiting for a toxicology report to determine the cause of death but say it was not suspicious.
Hugh Jackman, who worked with Ngoombujarra on Australia, expressed his sorrow on Twitter.
“So saddened to hear about the passing of David Ngoombujarra Starr. An extraordinary man, actor and friend,” he said.
“His laugh, warmth and humanity will live on with all who knew him.”
David Ngoombujarra was born in Meekatharra, in Western Australia’s midwest, in 1967 as David Bernard Starr. He was was raised in Coolbellup, in Perth’s south.
A member of the Stolen Generation, Ngoombujarra went on to become one of Australia’s best-known indigenous actors.
He won three Australian Film Institute awards for Blackfellas, Black and White, and The Circuit.
He also had roles in Crocodile Dundee in Los Angeles and Kangaroo Jack.