The 83-year-old actor, whose last Broadway appearance was as Herr Schultz in Cabaret, died of heart failure, and had been battling lung cancer, his agent Sheryl Abrams said.
Mr. Bosley played many stage roles in his long career, but was best known as Howard Cunningham, the head of household of the 1950s-set TV sitcom, "Happy Days" (1974-85). He later starred in the mystery series "The Father Dowling Mysteries."
In 2006, he starred in the Broadway tour of On Golden Pond opposite Michael Learned. His Broadway credits also include Beauty and the Beast (as Belle's father Maurice), the musical The Education of H*Y*M*A*N K*A*P*L*A*N (title role), Catch Me If You Can (a 1965 play), A Murderer Among Us (a 1964 play), Natural Affection (a 1963 play), the musical Nowhere to Go But Up (1962), The Beaux Stratagem (1959) and The Power and the Glory (a 1958 drama).
Mr. Bosley is heard on the original cast album of Jerome Bock and Sheldon Harnick's Fiorello!, a fictionalized account of the rise of charismatic New York City Mayor Fiorello H. LaGuardia.
In 2006, he told Playbill magazine, "It was amazing because I thought I was being considered for the understudy. The whole thing just went so fast. It took about six months to realize what was happening to me, and that I had a moment in my life that actors dream about. That show really became part of my personal life. I did it 15 years later with my wife, and I picked up the script and read the first line and threw the script away. I knew every line in the play — which I can't say has happened on other occasions." A publicist who issued a statement on behalf of the family, said Mr. Bosley is survived by his wife, Patricia Bosley, his brother Richard Bosley, his daughter Amy Baer, stepdaughters Kimberly diBonaventura and Jamie Van Meter and seven grandchildren.