Family members tell TMZ.com the star had been battling a staph infection, but further details regarding his death were unavailable as WENN went to press.
After serving in the U.S. Navy during World War II, Bosley made his stage debut in Our Town with Chicago's Canterbury Players.
He later shared the stage with Paul Newman at the Woodstock Opera House in Illinois, but his breakthrough stage role came in 1959 when he portrayed New York Mayor Fiorello H. La Guardia in Pulitzer Prize-winning musical Fiorello! The part won him a Tony Award.
But Bosley is perhaps best remembered for his role as patriarch Howard Cunningham on the hit TV sitcom Happy Days, which ran from 1974 to 1984.
He also landed a string of notable film and TV credits, including Murder, She Wrote and Father Dowling Mysteries, and more recently cameos in That '70s Show and One Tree Hill.
Bosley last appeared in 2010 comedy The Back-up Plan, starring Jennifer Lopez.