The actor -- who was best known for appearing in classics like "The Dirty Dozen," "M*A*S*H," "Animal House," "Hunger Games" and many, many other films -- passed away Thursday in Miami, Florida after a long illness ... something CAA announced.

No cause of death was shared, and the exact details of his passing weren't disclosed either.

His son, Kiefer Sutherland, confirmed the news on Instagram, writing ... "With a heavy heart, I tell you that my father, Donald Sutherland, has passed away. I personally think one of the most important actors in the history of film."

He continued ... "Never daunted by a role, good, bad or ugly. He loved what he did and did what he loved, and one can never ask for more than that. A life well lived."

Alongside the upload, Kiefer shared a black and white throwback pic of himself as a baby being held by Donald. The late actor was a father to 5 children, including CAA Media Finance exec Roeg Sutherland.

Born in New Brunswick, Canada ... Donald studied drama and engineering at Victoria University in Toronto -- later abandoning his engineering aspirations by moving to London, where he enrolled at the London Academy of Music and Dramatic Art.

In the mid-'60s, Donald broke into the British acting scene, appearing in a number of TV series -- including "The Saint," "The Sentimental Agent," etc. He then became a staple in war films ... thanks to his breakthrough roles in "The Dirty Dozen," "M*A*S*H" and "Kelly's Heroes."

Donald soon became a Hollywood staple ... with his most notable credits including "Klute," "Don't Look Now," "The Day of the Locust," "Fellini's Casanova," "Invasion of the Body Snatchers," "Ordinary People," "JFK," "Six Degrees of Separation," "The Italian Job," and "Pride & Prejudice."

Younger fans likely best know Donald for his work as President Snow opposite Jennifer Lawrence's Katniss Everdeen in the 'Hunger Games' franchise. His character was the subject of a blockbuster prequel flick last year, titled "The Hunger Games: The Ballad of Songbirds & Snakes" ... which saw Tom Blyth play a younger version of Donald's villainous character.

Donald was married 3 times over his lifetime, with his 3rd marriage to actress Francine Racette lasting over 5 decades. The legendary actor is survived by his aforementioned wife, kids, as well as four grandchildren.

He was 88.