Goodwin will join Swans coach Dean Cox as a director of coaching and performance after being axed by the Demons in August.
The 48-year-old brings a wealth of experience to the Sydney coaching box, with Cox entering his second year at the helm.
The Swans paid the price for a slow start to this year's season, finishing 10th (12-11) after a last-gasp effort to make finals failed.
Goodwin had been heavily linked to a move interstate, given wife Kristine works in Sydney.
GWS coach Adam Kingsley had left the door ajar for Goodwin, while West Coast coach Andrew McQualter also flirted with the idea of recruiting the former Adelaide champion.
Goodwin moves to the Swans after Melbourne announced Geelong assistant Steven King as his replacement last week.
"I'm absolutely thrilled to be joining Sydney as I've always admired how the Swans work hard and take care of their people," Goodwin said in a club statement.
"Sydney is a club that has achieved sustained success, and I'm looking forward to helping continue that tradition by developing the coaches and players who will shape the club's future."
Taking over from Paul Roos in a succession plan for the 2017 season, Goodwin led Melbourne to their first premiership in 57 years in 2021.
He moved into coaching after 275 games for the Crows, first serving as an assistant at Essendon.
Goodwin is a five-time All-Australian and a two-time premiership player but off-field turmoil and dwindling performances on the field placed his job as Melbourne coach in jeopardy.
Goodwin was let go after just seven wins this season.
Swans football boss Leon Cameron said Goodwin's character and experience made him the perfect fit for the club.
"He's a proven leader, a creative thinker, and someone who's passionate about helping our game grow," Cameron said in a club statement.
"A big part of Simon's job will be helping our coaches grow and develop, and we know his experience will be invaluable."
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