The 35-year-old, who was initially released after last season having suffered a serious knee injury, insists it was always his plan to stay at Old Trafford.
Ibrahimovic will wear the number 10 shirt recently vacated by Wayne Rooney on his return to United, having previously worn the nine jersey now taken by Romelu Lukaku.
The former Sweden international also announced his return to United in his own unique style on Twitter, depicting himself as a God-like figure arm-wrestling a red devil.
“I am back to finish what I started,” Ibrahimovic told the club’s website after he sealed his return on Thursday
“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.”
Ibrahimovic, whose season was cut short by his injury in April, scored 28 goals in all competitions in 2016-17 as United won the Europa League and EFL Cup.
The initial expectation was that Ibrahimovic would be out with injury until January, but club and player insist his recovery is going well, prompting hopes he could return to action sooner.
