Bosley died of heart failure at a hospital near his Palm Springs home. Bosley's agent, Sheryl Abrams, said he was also battling lung cancer.
TV Guide ranked Bosley's Happy Days character No. 9 on its list of the "50 Greatest TV Dads of All Time" in 2004. The show debuted in 1974 and ran for 11 seasons.
After "Happy Days" ended, Bosley went on to a recurring role in "Murder, She Wrote" as Sheriff Amos Tucker. He also was the crime-solving priest in television's "The Father Dowling Mysteries," which ran from 1989 to 1991.
When he was first offered the costarring role in "Happy Days," a series about teenage life in the 1950s, he turned it down.
"After rereading the pilot script," he recalled in a 1986 interview, "I changed my mind because of a scene between Howard Cunningham and Richie. The father/son situation was written so movingly, I fell in love with the project."
Propelled by the nation's nostalgia for the simple pleasures of the 1950s, "Happy Days," which debuted in 1974, slowly built to hit status, becoming television's top-rated series by its third season.
It made a star of Henry Winkler, who played hip-talking, motorcycle-riding hoodlum Arthur "Fonzi" Fonzarelli. His image initially clashed with that of Richie and his "straight" friends. But over the show's 11-season run Fonzarelli would transform himself from high school dropout to successful businessman.
After "Happy Days" ended, Bosley went on to a recurring role in "Murder, She Wrote" as Sheriff Amos Tucker, who was often outsmarted by Angela Lansbury's mystery writer, Jessica Fletcher.
His own series, "The Father Dowling Mysteries," ran from 1989 to 1991. The avuncular Father Frank Dowling was assisted in his detective work by nun Sister Steve, played by Tracy Nelson.
Although "Happy Days" brought him his widest fame, Bosley had made his mark on Broadway 15 years before when he turned in a Tony Award-winning performance in the title role in "Fiorello!" He also was the crime-solving priest in television's "The Father Dowling Mysteries."
His Broadway triumph depicted the life of New York's colorful reformist mayor of the 1930s and '40s, Fiorello La Guardia.
For two years, Bosley stopped the show every night when he sang in several languages, depicting La Guardia during the years the future mayor worked at New York's Ellis Island, aiding arriving immigrants.
The play won a Pulitzer Prize and Bosley received the Tony for best actor in a musical.
After failing to duplicate his success in "Fiorello!," Bosley moved to Hollywood in 1968. He would not return to Broadway until 1994 when he originated the role of Belle's father in Disney's production of "Beauty and the Beast."
In Hollywood, the rotund character actor found steady work appearing in the occasional movie and as a regular on weekly TV shows starring Debbie Reynolds, Dean Martin, Sandy Duncan and others.
During the 1990s, Bosley toured in "Beauty and the Beast" and "Show Boat," playing Captain Andy in the latter.
Bosley made only a handful of theatrical movies. Among them: "Love With the Proper Stranger," "Divorce American Style," "The Secret War of Henry Frigg," "Yours, Mine and Ours."
Born in Chicago in 1927, Bosley served in the Navy before returning to his hometown to study at De Paul University. Intrigued with acting, he enrolled at the Radio Institute of Chicago and began appearing in radio dramas. He made his theatrical debut in a production of "Golden Boy."
After moving to New York, he studied at the Actors Studio under Lee Strasberg.
After making his off-Broadway debut in "Thieves Highway" in 1955, he struggled to find other acting jobs, supporting himself as a temporary office worker, a doorman at Central Park's Tavern on the Green and a hat checker at Lindy's deli.
Then came "Fiorello!" in 1959.
Bosley married dancer Jean Eliot in 1962 and the couple had one child, Amy. Two years after his wife's death in 1978, Bosley married actress-producer Patricia Carr, who had three daughters from a previous marriage.