His daughter-in-law, Beth Morgan, told The Associated Press the actor died at his home in Brentwood after having pneumonia.
"He was side-splittingly funny, a very gent and loving father-in-law," Beth Morgan said. "He was very humble about having such a successful career."
Morgan appeared in mostly supporting roles on the big screen, playing opposite such stars as Henry Fonda, John Wayne, James Garner, Elvis Presley and Dan Aykroyd.
On television, he was more the comedic co-star, including roles on "December Bride," its spin-off "Pete and Gladys," as Sgt. Joe Friday's loyal partner in later "Dragnet" episodes and on CBS-TV's long-running "M-A-S-H" series, for which he earned an Emmy award in 1980.
Yet acting wasn't Morgan's first career choice.
Born in Detroit in 1915, Morgan was studying pre-law at the University of Chicago when public speaking classes sparked his interest in the stage. Before long, he was working with a little-theater group in Washington, D.C., followed by a two-year stint on Broadway in the original production of "Golden Boy," with Karl Malden and Lee J. Cobb.
Morgan made his way to Hollywood in 1942 "without any assurance that I would find work," he said in a 1976 interview with The Associated Press.
"I didn't have enough money to go back East, so I stayed around finding jobs mainly out of friendships."
He signed a contract with 20th Century Fox after a talent scout spotted him in the one-act play, "Hello, Out There."
One of his earliest films was "The Ox Bow Incident" in 1943 with Fonda. Other films included: "High Noon," "What Price Glory," "Support Your Local Sheriff," "The Apple Dumpling Gang" and "The Shootist."
Morgan began his television career in 1954 when the medium was in its infancy.
"Television allowed me to kick the Hollywood habit of typing an actor in certain roles," Morgan said, referring to his typical sidekick or sheriff portrayals on the big screen
In "December Bride," his first TV series, Morgan played Pete Porter, a perpetually henpecked neighbor. The CBS series lasted from 1954-1959, when he went on to star in his own series, "Pete and Gladys," a spinoff of "December Bride."
Demonstrating his diversity as a character actor and comedian, Morgan also starred in "The Richard Boone Show," "Kentucky Jones" and "Dragnet."
But it was his role as Col. Sherman Porter on "M-A-S-H" for which Morgan became best known.
"M-A-S-H was so damned good," Morgan told the AP. "I didn't think they could keep the level so high."
His acting career didn't stop after the popular series left the air in 1983 after 11 years -- one of television's most successful prime-time runs. Morgan went on to appear in several made-for-TV movies and other television series, such as "AfterMASH" and "Blacke's Magic."
When he was not on the set, Morgan enjoyed reading books about the legal profession and poetry. He also liked horses, which he once raised on his Northern California ranch.
Morgan is survived by three sons, Charles, Paul and Christopher; eight grandchildren and nine great-grandchildren.
No services have yet been planned.