The Swede's contract at Old Trafford has been terminated as he closes in on a move to LA Galaxy.
Ibrahimovic enjoyed a stunning debut season at United but a serious knee injury has prevented him getting back to that level.
"Everyone at the club would like to thank Zlatan for his contribution to the team since his arrival and wishes him well for the future."
Meanwhile, the Swede stated on social media: "Great things also come to an end and it is time to move on after two fantastic seasons with Manchester United.
"Thank you to the club, the fans, the team, the coach, the staff and everybody who shared with me this part of my history."