The New Zealand actor was surrounded by family when he died in Sydney on Monday, triggering a wave of tributes led by prime ministers, actors and film groups.
Neill earned a "special place in Australian hearts", Prime Minister Anthony Albanese said of the 78-year-old.
"Wry and dry, thoughtful and laconic, Sam fought illness with the same dignity, humour and conviction that gave strength to his every performance," Mr Albanese posted on social media.
"He will be much mourned and long remembered. May he rest in peace."
The Kiwi actor, who featured prominently in Australian films in a storied career that included roles in blockbusters Jurassic Park and Peaky Blinders, was remembered as "one of the greats" by New Zealand's Prime Minister Christopher Luxon.
"For more than 50 years he took New Zealand stories to the world and his talents helped make our film industry into what it is today – one of our greatest cultural exports," Mr Luxon said.
Neill's death was confirmed by his family in a social media post.
"The loss was sudden and unexpected but blessed by the fact that Sam remained cancer free," according to a post on Neill's official Instagram account.
"More details will be shared later, but for now, on behalf of the family, we ask that you respect their privacy as they navigate this immeasurable loss."
A cause of death was not specified.
American director Colin Trevorrow, who worked with Neill on reviving the Jurassic Park franchise, described him as a "beautiful man".
Screen Producers Australia said his contribution for pushing Pacific stories globally was immeasurable with an indelible legacy left behind.
"Sam Neill was one of the great figures of Australian and New Zealand screen," the body said in a statement.
"His extraordinary talent and professionalism enriched countless productions and inspired generations of filmmakers and performers."
Comedian and cancer survivor Magda Szubanksi offered an emotional tribute to her friend.
"I really don't have any words right now. I'm in complete shock. Last time we spoke he was going so well. My heart goes out to his family and all who love him - and there are so many of us. Vale my darling friend."
Neill was diagnosed with a rare, aggressive form of non-Hodgkin lymphoma in March 2022.
In April, he announced his cancer-free status after taking part in an Australian clinical trial.
Neill was one of a host of actors and directors who achieved international fame after an explosion of Australian films that began in the late 1970s but remains best known for his role in Jurassic Park.
His memoir Did I Ever Tell You This? came out in March 2023 and he was awarded a knighthood in recognition of his "outstanding contribution to film", a title approved by the late Queen Elizabeth II.
He is survived by four children and eight grandchildren.
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