Rosman was one of two Demons players that were delisted this year, with the 194-centimetre tall defender seeing his time in the red and blue come to an end after just two seasons.
The 20-year-old joined Melbourne as the 34th overall pick in the 2020 National Draft and was unable to break into Simon Goodwin's side.
After leaving the Demons at the end of September, Rosman has signed with Port Melbourne to continue his career.
Rosman played 15 matches for Melbourne's VFL affiliate side Casey in 2022 and averaged 11.3 disposals and 3.9 marks per game.
The Borough confirmed Rosman's signature on Friday, expressing their delight for the young backman to join their squad for next season.
"We went into the off-season with a specific focus on what we needed to add to our group and another tall defender was one, "Port Melbourne football manager Glenn Balmforth said in a club statement.
"So we are rapt to have Fraser join us and feel he will add some more quality to our defence with not only his ability to intercept but his rebound and ball use from defensive 50."
The Borough recorded seven wins from their 18 matches in the VFL this year to finish 16th on the ladder.