The 35-year-old former Sweden striker made 46 appearances and scored 28 goals for United last season. Ibrahimovic was released by the club in June after his season was ended prematurely by a knee injury, but he is expected to be fit again in December.
Jose Mourinho said that "After his contribution last season he deserves our trust and we will be patient waiting for him to return," "We are delighted Zlatan is on the road to recovery and we are equally delighted to have his ambition and experience back with us. "I have no doubt that he will be important in the second part of the season."
Ibrahimovic who had this to say: "I am back to finish what I started. It was always mine and the club's intention for me to stay. "I cannot wait to get back out on that Old Trafford pitch, but I also know that I have to take my time to make sure that I am ready. I have been working hard and will continue to do so to make sure I am in the best possible condition for my return to the pitch."