Ibrahimovic scored 29 goals in 53 games for United, who have agreed to an early termination of his contact, which was due to expire in the summer.
The 36-year-old former Sweden striker has played only seven times since damaging cruciate ligaments in April.
"It is time to move on after two fantastic seasons with Manchester United," he wrote on Instagram.
"Great things also come to an end. Thank you to the club, the fans, the team, the coach, the staff and everybody who shared with me this part of my history."
Announcing his departure, United said: "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."
Ibrahimovic joined the Premier League club from Paris St-German in 2016.
Earlier this month, United manager Jose Mourinho had said the striker was likely to leave at the end of the season.
The Swede, who re-signed for United on a one-year deal in August, returned to action in November after the knee injury that curtailed his first season at Old Trafford.
But he has not featured since the Premier League draw against Burnley on 26 December.
It has also been suggested he could come out of international retirement for Sweden at this summer's World Cup.
BBC Sport
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