The Lancashire-born star presented the darts-themed TV gameshow, which was watched by more than 12 million viewers, and obtained cult status among university students, for 15 years in the 1980s and 1990s.
After Bullseye he had other TV work come his way, including as Hoss Cartwright in the second series of Peter Kay's Phoenix Nights, Jonathan Creek, Muck and Brass and The Grimleys, as well as radio and stand-up gigs.
"He passed away very peacefully, she was with him".
His agent Patsy Martin told the Press Association: "I will very sadly miss Jim".
"It wasn't completely unexpected, he's been ill for several weeks in hospital".
His greatest love was his wife Phyllis with whom he has two children. "We are all shedding a tear", said his friend Pleus.More news: YouTube will fight conspiracy videos with Wikipedia links
More news: LeBron: I Get Better with Age
More news: Snow piles up in Northeast as blizzard begins winding down
"I've known him since the Bullseye days. He was a very lovely, genuine man".
"The Royal Lancaster Infirmary were wonderful, we couldn't have asked for better".
Comedian Jim Davidson said "RIP Jim Bowen".
"As with people getting on, Jim has had several strokes, one in 2011".
"You can't beat a bit of Bully".
Comedy greats including David Baddiel took to social media to pay tribute to Bowen, with Baddiel making a joke about God meeting Bowen and Stephen Hawking, who passed away on 13 March, at the same time.
Talking about the love he has for his family, Jim admitted to the Mirror a year ago: "I've had more than my share of good luck with a priceless marriage and family".