His death followed a 16-month battle against non-Hodgkin's lymphoma, a form of cancer of the blood.
A League Managers Association statement read: "Respected throughout the game by players, coaches and managers alike Gary will be sadly missed. Our thoughts and condolences are with Gary's wife Jacqueline and children."
Ablett won the league twice in 1987-88 and 1989-90, along with the FA Cup in 1989 with Liverpool, where he featured at left-back and later at centre-back.
He moved to Merseyside rivals Everton for £750,000 in 1991 after Kenny Dalglish resigned as manager to be replaced by Graeme Souness, going on to win the FA Cup again in 1995.
He later made over 100 appearances for Birmingham and finished his playing career in Australia, before moving into coaching. He managed Stockport for the 2009-10 season and had agreed to join the coaching staff at Ipswich before his disease was diagnosed.
Liverpool manager Kenny Dalglish, who gave Ablett his debut for the club, told Liverpoolfc.tv: "The most important thing just now is to pay our respects to Gary, his wife Jacqueline, the two boys and his wee girl.
"It's a sad, sad day for his family and everyone connected with Liverpool Football Club. Obviously he had a long battle and I'm sure it was a lot of suffering and a lot of pain for him, but the only thing you can say is at least he won't be suffering any longer.
"I gave Gary his debut and remember him scoring on his first start at Anfield against Nottingham Forest.
"He was a really good servant to the football club not only as a player, but also as reserve team coach.
"He served the club proudly and credibly. It's very sad for everybody."
Roy Evans, who was on the coaching staff at Liverpool throughout the late 1970s and 1980s and became manager from 1994 until 1998, lauded Ablett’s professionalism as a player.
“He was a really good professional, he never let you down,” Evans told Sky Sports News.
“[He was] never looking to do anything that was sensational, he just did his job. They’re the type of people in football that you have to take your hat off to sometimes.
“We all love to see great players do fancy things, but people like Gary Ablett, the steady Eddies of football, make a big contribution to the game.”
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