Mr Turner is a legend at both clubs. He passed away in April following a battle with dementia.
The match will be played at Peterborough's ABAX Stadium on August 1 (3pm kick-off).
"Chris was one of those rare breed of people who have played for and managed both Cambridge United and Peterborough.
The game is a chance for both sets of supporters to pay their respects and thank him for what he did for the two clubs, and we are looking forward to taking our team and supporters over to London Road.
In terms of what he achieved for Cambridge United, he signed many of the players that formed one of our most successful teams.
He loved by both clubs, was equally adored by many people and we look forward to the occasion doing his memory justice."
– Dave Doggett, Cambridge United Chairman
Learn more about Dementia here