Knapp, who lived in Danville, California, was hired by the Jets in January as part of new coach Robert Saleh's staff, serving as the passing game specialist. He was 58.
"Greg had such an inner peace about him that people always seemed to gravitate towards," Saleh said. "He lived life in a loving way that helped him connect with people from all walks of life in a unique way. In his short time here, I believe the people in this organization had a chance to experience that connection."
Knapp was struck while bicycling Saturday in the city of San Ramon, in the San Francisco Bay Area, and never regained consciousness.
The accident happened around 3 p.m., and the driver involved was said to be cooperating with the investigation. A preliminary investigation showed drugs or alcohol did not appear to be a factor in the crash.
He is survived by his wife, Charlotte, and three daughters, Jordan, Natalie and Camille.
"Greg's infectious personality is most people's first and lasting memory of him," said the Knapp Family in a statement. "The phrase "He never met a stranger" encapsulates Knapper's zest for life. He had a unique gift to make everyone feel special, and to Knapper, they all were."
Among Knapp's primary roles was to help develop quarterback Zach Wilson, the No. 2 overall draft pick.
Knapp had been settling in with the Jets' young quarterbacks room, helping to coach up Wilson, second-year QB James Morgan and third-year man Mike White, none of whom has played in an NFL game yet.
He had noted that Wilson is "a fast study...a big-time student of the game," and said he enjoyed working with his young room.
"It is really cool," he told reporters at last month's full-squad minicamp. "Both my parents are teachers. It's like, here's the canvas, start teaching them what you know without over-teaching them too quickly. So that's the challenge, but it's really exciting."
Prior to signing onto Saleh's Jets staff on Jan. 21, Knapp, on his second tour with Atlanta, spent three seasons as the Falcons' quarterbacks coach. Over that span, quarterback Matt Ryan passed for an NFL-high 13,971 yards with 87 touchdowns, 66.9% accuracy and a 97.7 passer rating.
Knapp also spent four seasons in Denver as the Broncos' QBs coach in 2013 and adding passing game coordinator to his title for 2014-16. Before the Broncos, he was offensive coordinator with Oakland (2007-08, 2012) and Seattle (2009).
He coached Houston's quarterbacks in 2010-11, and before Denver, he had his first hitch with the Falcons, serving as offensive coordinator from 2004-06 and helping them lead the league in rushing all three seasons.
Knapp also coached at his alma mater, Sacramento State, for nine seasons, after playing four seasons for the Hornets at QB. He was in multiple NFL training camps as a player and a coaching intern, including Kansas City (1986), the L.A. Raiders (1987-90) and the 49ers (1992-94), all while coaching at Sac State.
"In his short time with us, Greg had an immediate influence on those who had the pleasure of spending the smallest amount of time with him," Jets Chairman Woody Johnson said. "His legacy is not only working with some of the brightest quarterbacks the league has ever seen, but the countless others across this world he has had an indelibly positive influence on."
"Greg is such an amazing individual, it is hard to imagine the challenge facing him and his family," Saleh said in a statement immediately after the crash. "Greg's fun nature, kind disposition and wealth of knowledge has allowed him to make genuine connections with all of our coaches, players and staff since he has been here. I ask that you keep him in your prayers as we all pull for him to recover from this horrific accident."
Jets rookies reported to the team facility in Florham Park, New Jersey, on Tuesday, with the rest of the team scheduled to report for training camp July 27. The first camp practice is the next day.