The 26-year-old was cut by the Dogs this week, ahead of the first list lodgement deadline of 2pm on Thursday.
Daniel Cross, Patrick Veszpremi, Lukas Markovic and Nick Lower have already been told they won't be offered new contracts by the club for next year.
Cross is expected to be signed by Melbourne on Friday presuming he passes a medical at the club.
Addison was drafted by the Dogs in the second round of the 2005 NAB AFL Draft and made his AFL debut in round 20, 2006.
The hard-working midfielder from New South Wales played 88 games, including 12 this year.
"Dylan is a popular teammate and a high quality person, who gave his all for the team during his time here," list manager Jason McCartney said.
"We thank all players who have departed the club for their dedication and input that they've unreservedly given to our club, and sincerely wish them the best for the future."
The Bulldogs added Essendon's Stewart Crameri and Greater Western Sydney's Sam Darley to their list during the Gillette AFL Player Exchange Period.
They have selections 4, 42, 60 and 96 in next month's draft, which will be held on the Gold Coast on November 21.
Twitter: @AFL_JenPhelan
