Unrestricted free agent Silvagni, 27, is expected to join either Collingwood or the Western Bulldogs.
A father-son selection for the Blues, Silvagni played 128 games across 10 seasons since his 2015 debut.
He is the son of Blues great Stephen Silvagni, who played 312 games for Carlton, and the grandson of Sergio Silvagni, who made 239 appearances for the club.
"Whilst the decision was not easy to leave the football club, I felt the time was right to explore another opportunity," Silvagni said."I want to say a huge thank you to everyone at the club for their support during my time there, I sincerely appreciate the opportunity this club has given me and my family."
Silvagni shone as a key back this year on his return from an ACL tear and the Blues had unsuccessfully put a four-year offer to him.
"We made it really clear to Jack that we wanted him to remain a Carlton person, however as an unrestricted free agent Jack had a right to meet with a number of clubs and as a result has made his decision to pursue other opportunities, that is the reality of our industry in regard to player movement," list boss Nick Austin said.
"As we head into the upcoming trade, free agency, and draft period this affords us a number of options as we approach this time of year, and we will continue to make decisions that put the interests of the Carlton Football Club first and foremost."
Silvagni's exit follows fellow free agent Tom De Koning's anticipated departure for St Kilda on a bumper eight-year deal.
Earlier on Tuesday, assistant coach Aaron Hamill was among three more departures as Carlton continue their AFL football department "revamp".
Aaron Greaves, their head of coaching performance and innovation, is another football department casualty in the wake of their disastrous season, when they finished five wins out of finals contention.
The Blues decided to stick with senior coach Michael Voss, but football department boss Brad Lloyd also left at the end of the season.
Carlton rarely looked in finals contention this year after reaching a preliminary final in 2023 and making the top eight last season. Changes to the football department were inevitable.
Development and talent manager Tom Lonergan is also leaving for another job.
Hamill had been the Blues' backline coach for the last four seasons.
Greaves also joined Carlton in 2021 with Lonergan on board since 2023.
"Following today's announcement, the Blues will now look to revamp their coaching structure," Carlton said in a statement.
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