Conte took Juve to three consecutive Serie A titles from 2012 to 2014 - their first league trophies since the Calciopoli scandal - and also oversaw two Supercoppa Italiana wins.
The 44-year-old exited the Turin club by mutual consent on Tuesday and has been linked with the vacant Italy coaching job.
Agnelli hailed Conte's contribution to the club since May 2011as significant.
"You have been a great leader for our team and today's news saddens me immensely," Agnelli wrote in an open letter addressed to Conte published on Juve's official website.
"I think about the three years we spent together, the three years in which we rewrote this club's history: three Scudetti in a row, two Italian Super Cups, and perhaps more importantly a period of exponential growth."
Agnelli insisted life at Juve will go on, but he hopes Conte will remain a keen supporter of the club he made over 400 appearances for.
"Juventus will start again with a squad of highly talented, professional footballers who will give their all for the new coach and go on writing this club's present and future," Agnelli continued.
"You have been a part of Juventus' history and I know that whatever choice you make, hearing of a Juventus victory will always bring a smile to your face.
"I, together with all the players, the management and staff, will continue to work night and day, because that is no less than Juventus and Juventini deserve. And anyone who works at this club knows they must live up to its great tradition in every moment.
"Thanks for everything, Antonio."
