Cook, who played county cricket for Northamptonshire and has seven England Test caps to his name, helped steer Durham to three Championship titles and Friends Provident Trophy success.
He also oversaw the development of future stars such as Ben Stokes, Mark Wood, Steve Harmison, Graham Onions and Mark Stoneman.
The 66-year-old, who served as the club’s head coach between 2007 and 2013, said: “It comes with a heavy heart that I am leaving my role but I’m immensely proud of the work we have achieved during my 27-year stay.
“It’s been a privilege to work at Durham for so long and the memories will be with me forever.”
Chairman Sir Ian Botham paid tribute to Cook’s contribution to Durham’s emergence as a first-class county side.
He said: “Geoff is a true legend of the club and his instrumental work has had an immeasurable impact on the success of the club.
“His efforts in establishing Durham as a first-class county and turning the team from newcomers to a title-winning force will never be forgotten, alongside his superb coaching achievements.”
Cook’s departure as part of staff restructure was announced just days after all-rounder Paul Collingwood revealed that he was to call time on his 23-year playing career at the end of the season.
England are preparing to name their limited-overs squad for the forthcoming tour of Sri Lanka, with national selector Ed Smith unlikely to veer too far from a tried and trusted white-ball unit.
The party will be national selector Smith’s first overseas pick since taking the reins earlier this year. Eoin Morgan’s men will play five one-day internationals in October, followed by a solitary Twenty20 on the island.