The actor died of natural causes at his home on Saturday. He had suffered ill health since a severe stroke in 2008.
Garner famously played the laconic private investigator Jim Rockford.
He won an Emmy for the role in 1977 and starred in 122 episodes of the hugely successful show from 1974 to 1980.
He returned to it in the 1990s with eight Rockford Files TV movies.
In 1963's iconic World War Two film The Great Escape, Garner played Flight Lieutenant Robert Hendley, an American in the RAF, alongside Steve McQueen, Richard Attenborough and Donald Pleasence.