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.
"After his contribution last season he deserves our trust and we will be patient waiting for him to return," said manager Jose Mourinho.
Ibrahimovic, who initially joined the Red Devils on free transfer in July 2016, had been recuperating at United's training ground after having knee surgery.
Mourinho added: "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 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." PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How I Made Me =N=2.5 MILLION In 7 Days from 2 Common Product I Imported and how you can do the same. Click HERE FOR FREE Details right now Warning To Men: This 3 Foods Is Killing Your Erection. Click Here To Know Them Secret Fruits that increased my Manhood and makes me last 55 minutes+ all time - Click here to get it Warning: Got Arthritis? 3 Simple Ways To Get Cured And Be Permanently Free From Joint Pains. Click Here To See Them REVEALED!! Reduce Your Blood Sugar Level And Reverse Diabetics Within A Short Period Of Time. Click Here To See How MIDNIGHT,Pressed Mr Kilanko Suddenly Couldn't Urinate. Shrink your Enlarged Prostrate Here! Click Here Now