The Northern Ireland-born New Zealand actor was best known for his leading roles in the blockbuster dinosaur franchise and The Piano, and appeared in more than 50 films over his career.
The family of the screen star, who was one of New Zealand's most successful Hollywood exports, said his death had been "sudden and unexpected" in a statement on Monday.
Neill was diagnosed with stage three angioimmunoblastic T-cell lymphoma, a rare type of non-Hodgkin lymphoma, in 2022.
After his cancer diagnosis, Neill said he would take a short break from acting, and had announced he was cancer free earlier this year.
His family said he died on Monday in Sydney, Australia, but did not specify the cause of death.
"Sam was surrounded by family and passed with the dignity that has characterised his whole life," they said.
"The loss was sudden and unexpected but blessed by the fact that Sam remained cancer free."
Neill was regarded as a versatile actor, who had traversed blockbuster and art house film throughout his career.
His range saw him dodge velociraptors in Jurassic Park, chop off actress Holly Hunter's finger in The Piano, and gouge out his eyes in the sci-fi film Event Horizon in his on-screen roles.
'One of the greats'
Tributes flooded in for Neill from around the world, from Hollywood directors to prime ministers.
Colin Trevorrow, who directed Neill in Jurassic World Dominion, remembered the actor as a "deeply soulful and beautiful man".
"He was a friend and collaborator at a challenging time, and his strength gave us all strength," he said.
He added: "It's not every lifetime you get to befriend a legend."
New Zealand Prime Minister Christopher Luxon described Neill as "one of the greats".
"He started out when there was barely a film industry in this country to speak of," he said.
"For more than fifty 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.
"His work will be watched and loved long after all of us."
In a post on X, Australian Prime Minister Anthony Albanese said: "Sam Neill starred in so many beloved Australian stories and he earned a special place in Australian hearts.
"Wry and dry, thoughtful and laconic, Sam fought illness with the same dignity, humour and conviction that gave strength to his every performance. He will be much mourned and long remembered."
Australian actor David Wenham said: "Aside from being an international all-round legend. Sam was the kindest, cheekiest, most generous and supportive friend going around."
Author Kathy Lette remembered Neill as a "wonderful actor but also the most charming, kind, intelligent and deliciously self-deprecating friend".
Australian comedian Magda Szubanski said: "An exceptional man - talented, kind, classy, wryly hilarious and loving. Proud cancer survivor. My heart goes out to all Sam's family and friends."
From Omagh to Hollywood
Neill was born Nigel John Dermot Neill in Omagh, but moved to New Zealand aged seven when his father retired from the army.
At the age of 11, he changed his name to Sam.
In his 2023 memoir, he said "to land in a primary school with a plum in the voice and Nigel for a name was asking for trouble".
He described himself as a nerdy, unsporty and stuttering boy, but took his first steps into acting through school plays.
His big break came with the low-budget 1977 New Zealand film Sleeping Dogs, which led to bigger roles in neighbouring Australia.
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. These included Paul Hogan, Mel Gibson, Geoffrey Rush, Russell Crowe, Jane Campion, Peter Weir and Gillian Armstrong.
He first came to the attention of international audiences in Armstrong's 1979 film My Brilliant Career.
Neill later appeared in the 1989 thriller Dead Calm, also starring a then-relatively unknown Nicole Kidman.
He twice co-starred with Meryl Streep in Australian director Fred Schepisi films Plenty and A Cry in the Dark, based on the true story of a dingo killing a baby in the Australian Outback.
He missed out on a chance at mega-stardom in the mid-1980s when he did a screen-test for the role of James Bond but did not land the role.
He would later achieve blockbuster fame in Steven Spielberg's 1993 hit Jurassic Park, as palaeontologist Dr Alan Grant.
Younger audiences will remember Neill for his portrayal of ruthless chief inspector Chester Campbell in Peaky Blinders.
Read more from Sky News:'Nothing to suggest' Ann Widdecombe murder politicalAntiques Roadshow star Theo Burrell dies aged 39
In 2022, Neill accepted a knighthood for outstanding contribution to film.
Neill, who was married twice, divided his later years between Australia and his vineyard in New Zealand's Central Otago, which produced Pinot Noir under the label Two Paddocks.
He is survived by his two sons and two daughters.
