The Swedish superstar looked to have kicked his last ball for United when he broke down with damaged knee ligaments in April.
Ibrahimovic travelled to America to undergo an operation and was expected to be sidelined until the start of 2018.
United bosses decided to release the veteran striker after rejecting the chance to trigger a 12-month extension in his £300,000-a-week deal.
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But Ibrahimovic was allowed to return to Manchester to use the club's Carrington training ground for his rehabilitation.
He is ahead of schedule in his recovery and now United bosses have decided to hand him a new contract on lesser terms, as Starsport reported earlier this week.
Ibrahimovic, 35, who scored 28 goals in his first season with United, insists he is on a mission to help Jose Mourinho's men win the Premier League title.
He said: "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."
Mourinho said: "We are delighted Zlatan is on the road to recovery and we are equally delighted to have his ambition and experience back with us.
"After his contribution last season he deserves our trust and we will be patient waiting for him to return.
"I have no doubt that he will be important in the second part of the season."
