Ablett, a member of Everton's FA Cup-winning side in 1995 after joining them from Merseyside rivals Liverpool, had been ill for the last 16 months after being diagnosed with non-Hodgkin's lymphoma, a cancer that affects the blood, in 2010.
The defender is the only player to have won the FA Cup with both Liverpool and Everton and, after retiring from the game, Ablett enjoyed a successful spell as a coach at both Anfield and Goodison Park before his only managerial appointment at Stockport.
A statement from Everton said: "Everyone at Everton was saddened to learn of the death of Gary Ablett.
"The thoughts of everyone at Everton are with Gary's family and friends at this tragic time."
Former Liverpool manager Roy Evans told Sky Sports News: "It's a big shock. Obviously we know Gary's been ill for a while. It's a really sad day.
"He was good at everything he did as a player. He made a big contribution to the game.
"He went into coaching and stamped his personality onto that and was doing a very good job, certainly at youth level. I remember he had bit of a difficult first spell at Stockport, but overall he's had a great career in football, he's a big loss to the sport."