Scott served under more than 12 managers during his near half-century at Pittodrie before retiring in August 2003.
Aberdeen chief executive Duncan Fraser said: "It is with tremendous sadness that I learned of Teddy Scott's death."
He added: "Teddy served the club for 49 years in every capacity imaginable.
"Although Teddy retired some eight years ago he remained close to the club and in particular Jim Warrender and Jim Crawford whom visited him regularly.
"Everyone at Aberdeen FC sends their deepest condolences to Teddy's family and friends."
Scott, a central defender, signed for Aberdeen in March 1954, playing once for the first team.
He was better known for his role as a trainer, then coach, firstly with the reserve team, where he nurtured young talent, before becoming kit man.
Sir Alex Ferguson took a full-strength Manchester United team to play Aberdeen for Scott's testimonial in January 1999, during their treble-winning season.