Ablett, a member of Liverpool's FA Cup-winning side in 1989 who went to enjoy more success at Merseyside rivals Everton, 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 Liverpool said: "Liverpool Football Club were today saddened to learn of the death of former player Gary Ablett. The staff of Liverpool FC would like to send our condolences to the family and friends of Gary."
Former Reds 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."
David Fairclough, who played for Liverpool between 1974 and 1983, added: "He was a lovely lad, he always conducted himself in the right way. He was great with people, always personable. What always came through with Gary was his attitude was just always very, very right."