Knapp, 58, was an avid cyclist who was riding Saturday in San Ramon in Northern California when a motorist swerved into the bike lane and hit him, said his agent, Jeff Sperbeck.
He never regained consciousness and died Thursday surrounded by his wife, his three daughters, his mother and his brother.
"Greg's infectious personality is most people's first and lasting memory of him," Sperbeck said 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."
San Ramon police said Thursday they're still investigating the crash that involved a 22-year-old man behind the wheel. Drugs and alcohol do not appear to be involved but police said they still want any witnesses to step forward.
The fatal collision happened a little before 2:49 p.m. Saturday on Dougherty Road just north of North Monarch Road, as the driver stopped and "cooperated with investigators," police said.
"Sadly Mr. Knapp succumbed to the injuries he sustained in Saturday's collision," San Ramon police said in a statement. "Our sincere condolences are with Mr. Knapp's family and loved ones."
The coming season would have been Knapp's first with the Jets. He and new head coach Robert Saleh were hired in January in a staff shake-up in hope of ending the franchise's five straight years of losing records.
Saleh offered his condolences to Knapp's family, saying Knapp was able to deeply connect with people even in his short time with the Jets.
"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."
Knapp, the team's passing game specialist, had been set to coach rookie quarterback Zach Wilson, a Brigham Young University prodigy whom the Jets selected with the second overall pick of this past NFL draft.
Knapp has been a fixture on NFL coaching staffs for the past 25 years, serving as quarterbacks coach or offensive coordinator for some of the league's best-known passing attacks.
He was quarterbacks coach with the Atlanta Falcons, working alongside four-time Pro Bowl signal caller Matt Ryan, for the past three seasons.
Before going to Atlanta, Knapp was the quarterbacks coach and passing game coordinator for the Denver Broncos, for whom he worked with Peyton Manning. Knapp's three seasons in Denver included the Broncos' victory in Super Bowl 50.
Brandon McManus, a kicker for the Broncos, mourned Knapp on Twitter on Thursday, calling him an "awesome" person.
"RIP Coach Greg Knapp. Always enjoyed our conversations on and off the field," McManus said.
Troy Taylor, head coach at California State University, Sacramento, said the school was "heartbroken," recalling Knapp's history as a Hornet.
"Greg was not only a great former Hornet player and coach, but one of the kindest and most generous people that I've ever known," Taylor said in a statement Thursday. "His success and humility have been an inspiration to all of us here at Sacramento State. We will continue to carry on his legacy within our football program and wish his family and friends peace and comfort through this difficult loss."
Knapp, who began attending Sacramento State in the fall of 1983, played quarterback and is ranked eighth in school history in career passing yards.
The Las Vegas Raiders, for whom Knapp was an offensive coordinator when the team was based in Oakland, said they were "saddened and stunned."
"The thoughts and prayers of the entire Raider Nation are with Coach Knapp's family during this extremely difficult time," the team said.