Holm died peacefully Friday morning in a hospital, surrounded by his family and carer, his agent, Alex Irwin, said in a statement. His illness was Parkinson's related.
A star of stage and screen, Holm won a Tony Award for best featured actor as Lenny in Harold Pinter's play "The Homecoming" in 1967.
An established figure in the Royal Shakespeare Company, he won a Laurence Olivier Award for best actor for his performance in the title role of "King Lear" in 1998.
He won a British Academy Film Award and gained a supporting-actor Oscar nomination for portraying pioneering athletics coach Sam Mussabini in the hit 1982 film "Chariots of Fire."
He also appeared in "The Fifth Element," "Alien,'' "The Sweet Hereafter,'' "Time Bandits,'' "The Emperor's New Clothes'' and "The Madness of King George.'' More recently, he portrayed Bilbo Baggins in "The Hobbit" and "The Lord of the Rings" trilogies.
Holm was knighted in 1998 for his services to drama.
"His sparkling wit always accompanied a mischievous twinkle in his eye," Irwin said. "Charming, kind and ferociously talented, we will miss him hugely.''
Holm was married four times and had five children.