Monfries will return home after Port gave up pick 48 to the Bombers, who he played 150 games for after being drafted in 2004.
The 25-year-old was used mostly as a forward in his eight seasons at Essendon but struggled to find his best form in 2012.
Port opted to agree to a trade instead of acquiring him as a restricted free agent to ensure they will receive the best compensation they can for losing Danyle Pearce (Fremantle) and Troy Chaplin (Richmond).
Port Adelaide general manager of football Peter Rohde said he was looking forward to having Monfries play a role in the middle of the ground next season.
"Angus is a player with great character who has been shown to have a really good record of durability throughout his time at Essendon," he said.
"He will bring us flexibility, too, because although he's played most of his AFL football as a forward, we can see him getting regular opportunities and performing to a high standard in our midfield as well as going forward.
"Angus was very highly rated when he was first drafted and we have certainly always held him in that regard."
Monfries said the challenge of helping Port become successful was one of the reasons behind his move.
"I'll miss Essendon, but it will be great to come home and play in front of my family and friends and help Port Adelaide get back to where it wants to be. That challenge is a big part of the appeal for me," he said.
"I am someone who likes to get the best out of themselves and coming to Port Adelaide I'll work to get more opportunities to do that.
"I think I can play a number of roles. I can play up forward but I am confident that I can push up into the midfield and get more involved in games."
Essendon coach James Hird said the club put an offer in front of Monfries to keep him at Windy Hill, but it was less than what were the Power were willing to pay.
"Angus has been a fantastic player for the Essendon Football Club, and it's always sad to see a player of his calibre leave," said Hird.
"At the end of the day Angus had an offer in front of him that we believe truly reflected his position at Essendon, but he has made a decision to secure his financial future and we have to respect that."We thank Angus for all his hard work over the years, and we wish him all the best for the next chapter in his career."