The 35-year-old Swede joined United on a one-year deal as a free agent last season and scored 28 goals in 46 appearances for Jose Mourinho's side before suffering a knee ligament injury in April.
"We are delighted Zlatan is on the road to recovery and we are equally delighted to have his ambition and experience back with us," Mourinho said in a statement on United's website.
"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."
Ibrahimovic, who helped United to win the League Cup and Europa League in his debut campaign in England, said he was keen to finish what he had started at Old Trafford.
"It was always mine and the club's intention for me to stay," he added. "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."
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