The 60-year-old was in charge at the Hamilton-based side for the past two seasons and guided them to the Super Rugby quarter-finals on both occasions.
"We are grateful to Coops for his outstanding leadership and coaching," the team's chief executive Michael Collins said in a statement.
"He is a proud man who set an incredibly high bar in terms of personal standards and behaviour, both on and off the field.
"We are really proud of the culture he has fostered inside our club and team environment, and he can be proud of what he has achieved."
The start of a new World Cup cycle from next season was a factor in Cooper's decision, New Zealand Rugby Chief Executive Steve Tew said.
"Next year is a post-World Cup year when there is a lot of player movement within Super Rugby and clubs are beginning the next four-year cycle," said Tew, whose organisation has a say in employing the Super Rugby coaches.
"Taking that into consideration, both Colin and the club have spoken at length over several weeks and agree that the time is right for a new coach to take the... Chiefs into 2020 and beyond."
Cooper, who was in charge of the Wellington Hurricanes for eight seasons before coaching provincial side Taranaki from 2010-2017, succeeded Dave Rennie at the Chiefs.
"The role of the head coach has evolved so much over the past five or six years," Cooper said.
"My passion is hands-on on-the-field coaching, but with bigger playing numbers and more staff involved these days, I am getting taken further and further away from my passion."
Former Waikato stalwart Warren Gatland, who is leaving the Wales job after this year's Rugby World Cup in Japan, had previously said he was interested in returning to a Super Rugby coaching role in New Zealand.
Gatland, however, was re-appointed earlier this month as British and Irish Lions coach for their 2021 tour of South Africa.
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
