He was a reserve player at Derby before his career was ended by injury.
Guthrie became the Rams' trainer and then kit manager, working with more than a dozen managers including Brian Clough over the course of six decades.
He was appointed an MBE in 2009 for services to football and has a stand named after him at the iPro Stadium.
Despite falling ill four years ago, he was still a regular on match days and usually sat in his familiar seat in the home dugout until very recently.
"It goes without saying everyone at Derby County is saddened to learn of the passing of Gordon," said Sam Rush, the club's president and chief executive.
"Our thoughts and condolences are with Gordon's family and friends at this time."
A minute's silence will be held in memory of Guthrie prior to Derby's EFL Cup third-round tie against Liverpool on Tuesday.
Former striker Andy Garner, who began his career at Derby and more recently was part of their coaching staff, said Guthrie was like a father figure to youngsters at the club.
"I found it quite daunting, being a young man and coming to Derby from a small village," Garner told BBC Radio Derby.
"Although I was a big, strong lad, I needed somebody like Gordie. I was lonely at times and he definitely helped me.
"It was a joy for me. I absolutely loved my two-year apprenticeship and Gordie was always there for us. The players and the staff all loved him being there."
Derby County's longest-serving staff member Gordon Guthrie MBE, who spent more than 60 years with the club, has died at the age of 86.