South Australian Premier Steven Marshall paid tribute to the actor in a statement late on Monday.
"It is with deep sadness that I share with the people of South Australia the passing of an iconic, once-in-a-generation artist who shaped the history of Australian film and Aboriginal representation on screen – David Dalaithngu," Mr Marshall's statement said.
"David Dalaithngu was from the Mandhalpingu clan of the Yolngu people, and was raised in the traditional ways in Arnhem land. In his later years he was a resident of Murray Bridge. He was a brother, son, friend, father, grandfather and husband.
"An actor, dancer, singer and painter, he was also one of the greatest artists Australia has ever seen."
Hugh Jackman remembered Dalaithngu's contribution to film as "immeasurable".
"I join all Australians, and the world over, in mourning the loss of David...Dalaithngu. One of the great privileges of my life was to work with David on the movie Australia," the actor wrote on Instagram.
"From his cheeky laugh, to that mischievous glint in his eye and effortless ease in front of the camera … His humanity is irreplaceable."
Olympian Cathy Freeman posted on Twitter "Thank you for the inspiration."
Thousands of fans and admirers took to social media platforms to farewell the actor, known as "uncle" to many Indigenous people.
"So very sad to hear the passing of our Uncle and I say our uncle coz to every Aboriginal kid in the 80s, 90's that's how we felt," one posted on Instagram.
His face would literally light up the screen his voice would make you escape from the reality of racism in our lives, he was our Denzil Washington, our Black Panther he was & still is our Hero."
Born at Maningrida in Arnhem Land on 1 July, 1953, David Dalaithngu grew up among the Yolngu people, becoming a skilled tracker, hunter and ceremonial dancer.
It was his ability as a dancer that gave him his big break as a 16-year-old. It brought him to the notice of visiting British filmmaker Nicolas Roeg, who handed him a leading role in the 1971 movie Walkabout.
Opposition Leader Anthony Albanese paid tribute to Dalaithngu on Twitter, remembering him as a "remarkable and powerful presence.
"Actor, dancer, painter and proud Yolngu man, he walked tall in two worlds with grace, truth and humour. Now he walks in another place," Mr Albanese wrote.
Former Senator and publisher Derryn Hinch recalled meeting Dalaithngu in New York after the movie was released.
"I was privileged to show David around New York on his first overseas trip to promote the movie Walkabout 50 years ago. Vale," he tweeted.
The film and Dalaithngu were smash hits, and the actor travelled the world to promote the film, meeting famous entertainers like John Lennon and Bob Marley along the way.
He went on to star in a string of Australian box office hits including his "favourite" Storm Boy in 1976, The Last Wave a year later, Crocodile Dundee in 1986 and Rabbit-Proof Fence in 2002.
He also appeared in Baz Luhrmann's Australia in 2008 after acclaimed performances in arthouse films got his stalled career back on track.
They included the 2002 movie The Tracker, which he considered his "best film," portraying the relationship between white and Indigenous men in the early 1900s, as well as Ten Canoes in 2006, which showed Aboriginal culture before white settlement, and Charlie's Country in 2013, which followed the demise of an Indigenous man.
The low-budget Ten Canoes, based on a traditional tale of love and revenge, won him a special jury prize at the Cannes Film Festival for best actor in innovative filmmaking.
Variety described him as "an actor capable of mischievousness and gravitas, often within the same shot" and Screen International said he had crowned his career with "a mesmeric portrait".
Dalaithngu was appointed a Member of the Order of Australia in 1987 and was awarded the Centenary Medal in 2001. In 2005 he was named Northern Territory Australian of the year.
Twice he received the Australian Film Institute award for best actor in a leading role, for The Tracker and Charlie's Country, and was nominated for best supporting actor for Rabbit-Proof Fence.
He was nominated for a Helpmann Award in 2004 for best male actor in a play for the production Gulpilil.
He was also celebrated in art when Craig Ruddy's portrait of him won the 2004 Archibald Prize.
Mr Marshall said his thoughts were with Mr Dalaithngu family and friend and carer Mary Hood.