"To the world, he was a legend, an actor from the golden age of movies who lived well into his golden years, a humanitarian whose commitment to justice and the causes he believed in set a standard for all of us to aspire to.
"Kirk's life was well lived, and he leaves a legacy in film that will endure for generations to come, and a history as a renowned philanthropist who worked to aid the public and bring peace to the planet," he added, saying he was "so proud" to be his father's son.
Michael's wife, Welsh actress Catherine Zeta Jones, paid her own moving tribute.
She wrote: "To my darling Kirk, I shall love you for the rest of my life. I miss you already. Sleep tight..."
Douglas, born Issur Danielovitch of Russian-Jewish ancestry in New York, made more than 90 films in a career that stretched seven decades.
Hits such as Spartacus and The Vikings made him one of the biggest box office stars in the 1950s and 1960s.
He was nominated for an Oscar for best actor in 1959 for his role as boxer Midge Kelly in Champion.
He also earned two Oscar nominations as a producer for The Bad And The Beautiful in 1953 and Lust For Life in 1957.
He acted alongside John Wayne in three films - In Harm's Way, Cast A Giant Shadow and The War Wagon and even earned $50,000 for saying the only English word at the end of a Japanese TV commercial: coffee.
But he said that, more than any of his films, he was most proud of his major role in breaking the Hollywood blacklist: actors, directors and writers excluded professionally because of links to the communist movement in the 1950s.
He hired and credited Spartacus's communist screenwriter Dalton Trumbo, writing in a book published in 2012 that he had "spent months thinking of some way to break (the blacklist).
He said he had told Trumbo: "When (Spartacus) is in the can, not only am I going to tell them that you've written it, but we're putting your name on it... your name, Dalton Trumbo, as the sole writer.
"I could feel my heart pounding. Even as I was saying the words, I was still trying to convince myself that this was worth the risk... The blacklist is broken."
Douglas survived a helicopter crash in 1991 and a stroke five years later.
The stroke left him with slurred speech and damaged facial nerves but did not stop him from attending the Academy Awards two weeks later to receive a Lifetime Achievement Award.
He continued to take small acting roles but said the stroke left him suicidal.
"Humour saved me," he told Parade magazine in 2014. "At first, I thought my life was at an end. But when I put the gun in my mouth, it hit a tooth. Ow! And that struck me funny. A toothache was stopping me from committing suicide?"
Source: Sky News