The veteran star died on Saturday at his home in Los Angeles. It is believed he had been in ill health after suffering a stroke four years ago.
No further details of the circumstances of his death have emerged.
Garner was best known for his Emmy Award winning role in the 1970s series The Rockford Files, as well as roles in Maverick, the Great Escape, and more recently in the romantic drama The Notebook, which also starred Ryan Gosling and Rachel McAdams.
Hollywood actor Tom Selleck, who guest-starred in The Rockford Files, said: "Jim was a mentor to me and a friend, and I will miss him."
The Star Trek star William Shatner said: "Sending thoughts and prayers to the family of James Garner this morning."
Sally Field, who co-starred with Garner in the romantic comedy Murphy's Romance, said: "There are few people on this planet I have adored as much as Jimmy Garner.
"I cherish every moment I spent with him and relive them over and over in my head. He was a diamond.''
Many stars also paid their respects to the star via social media, with director Ron Howard writing on Twitter: "RIP James Garner. Admired by all who knew him. When starring in Grand Prix the people around F1 said he had the talent to be a pro driver."
Actress Marlee Matlin, who appeared with Garner in a 1997 TV movie, Dead Silence, wrote: "Sad to read my dear friend and co-star James Garner passed. RIP sweet Jim Rockford."