Bosley died of heart failure at a hospital near his Palm Springs home at around 4 a.m. Tuesday. 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.
Fellow "Happy Days" cast member Ron Howard released a statement, praising the late actor, and expressing grief at his passing. The famed Hollywood director, who was a only teen when he played Richie Cunningham in the popular 70s show, described Bosley as "a great father and husband, and a wonderful artist" and that "Tom's insight, talent, strength of character and comic timing made him a vital central figure in the 'Happy Days' experience."
"My last conversations with Tom reflected the love of life and peace of mind that he always maintained throughout his full and rewarding life. I miss him already," Howard said in the statement.
"Tom was a talented professional in front of the camera and behind the scenes. He provided a positive influence over all of the young actors on 'Happy Days,'" said Garry Marshall, creator and executive producer of "Happy Days."
"Audiences will never forget the lovable Howard Cunningham who made us laugh on Tuesday nights. He was a good friend. I will miss him. Comedy will miss him," Marshall said.
The show debuted in 1974 and ran for 11 seasons.
"He was my husband of 11 years and the father of the company in many ways. He was so smart, he could make up a new end to fix a scene on the spot. We made a perfect couple. I played piccolo to his tuba," said actress Marion Ross.
Henry Winkler and Scott Baio, who both costarred with Bosley on "Happy Days," said they remembered the actor as "a great man."
"The Winkler family sends the most positive thoughts to the Bosley family at this very sad time," Henry Winkler told Eyewitness News. "He was great to work with, great to play charades with ... just a wonderful, wonderful gentleman."
Baio said he was a good man who taught him a lot about the business.
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.
The Associated Press contributed to this story.