Turner, who spent nine years as a player with Posh before winning back-to-back promotions as manager in the early 1990s, was diagnosed with frontal lobe dementia in 2006.
His wife Lynne previously said doctors told her the illness was "caused by heading too many balls".
Turner also played for Cambridge United, Luton, Swindon and Southend.
He started his playing career at Peterborough in 1969 and made more than 300 appearances.
His playing career also included time in the US.
Turner retired as a player in 1984 and took over as boss at Cambridge United a year later, managing them until 1990.
His successful reign at Peterborough ended in 1992, when he stood down to become chairman.
Mick Halsall, who captained Peterborough to victory in the play-off final in 1992, said Turner was a "great, great leader".
"He had a great ability to nurture," Halsall said.
"[We were] a bunch of scallywags who achieved so much, and in my opinion wouldn't have achieved it under anyone else."
Bob Symns, Peterborough chief executive, said Turner was "a legend who'll never be forgotten".
John Beck, who was brought to Cambridge as a player by Turner in 1986 and went on to take the club to the brink of the Premier League as manager, said Turner was a "very lovable man".
"I'd gone to meet the manager at Peterborough and I was going to sign, but then I got a phone call from Chris," he said.
"I went down to the Abbey (Stadium) and knew instantly that this was the man I wanted to sign for.
"He was just a wonderful person. Great warmth, great fun, great personality."
Former Peterborough United and Cambridge United manager Chris Turner has died, aged 64.