The Giants have confirmed Silvagni will step down after the draft, which will be held at the Gold Coast on November 27.
Last month Silvagni was linked to a move to Carlton, the club where he played 312 games and won two premierships before his retirement in 2001.
On Monday, the Giants confirmed Silvagni would be departing after next week’s draft.
"Stephen has helped build a very talented playing list to give this club every chance of success over the coming years," the Giants' general manager of football Graeme Allan said.
"This month's draft will be his fourth and he has decided this is now a good time to move on. We thank him for the important contribution he has made to help establish the Giants and wish him and his family all the very best."
Silvagni said: "It's been a privilege to be part of the Giants and work with a tremendous group of people. I have no doubt the club has a great future and I will follow its progress with interest."
The Giants currently hold three treasured first-round draft picks - selections four, six and seven, as well as picks No.23 and 24 in the second round.
Click here to see this year's indicative draft order
Silvagni joined GWS as list manager in 2011, the season before the club debuted in the AFL.
Meanwhile, Australian cricketer Simon Katich has been promoted to football operations manager at GWS.
The former Test opening batsman last year joined the club as a player development coordinator and match day runner.
He has been given an expanded role working under Allan.
"In just 12 months, Simon has proven to be a great asset for the club and we want to continue to develop his skills and believe this is an ideal role," Allan said.