Conte steered The Old Lady to three consecutive Serie A titles during his time at the helm, while also picking up the Italian Super Cup on two occasions.
However, the 44-year-old has now decided to leave his post just a day after the start of the club's pre-season, and Agnelli bemoaned the loss of a "great leader".
"Dear Antonio, you have been a great leader and this news saddens me greatly. Three years together have led us to write history with three consecutive titles and two Italian cups," he told the club's official website.
"You have given a group of highly talented professionals who will be at the disposal of the new coach to continue writing the future.
"You are in the history of the Bianconeri colours and whatever choice you make, a Juventus victory will always make you smile. Antonio, thank you for everything. Til the end."
Conte has been linked with the vacant Italy post after Cesare Prandelli stepped down following a disappointing World Cup.