His daughter-in-law Catherine Zeta-Jones led the tributes, writing: "To my darling Kirk, I shall love you for the rest of my life. I miss you already."
Tributes also came from director Steven Spielberg, Star Wars actor Mark Hamill and Breaking Bad star Bryan Cranston.
Douglas, who played the title role in the 1960 classic Spartacus, enjoyed a career that spanned seven decades.
Spielberg said Douglas left behind a "breathtaking body of work".