Manchester United released Ibrahimovic at the end of the season after the 35-year-old sustained a serious knee injury.
But, after wowing Old Trafford medics with his speedy recovery, the Red Devils have snapped him up on a one-year deal.
Explaining his decision to return, Zlatan 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.
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“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 scored 28 goals for United last season, helping the club win the EFL Cup and Europa League.
The former Paris Saint-Germain star will wear the No10 shirt for the forthcoming campaign.
Romelu Lukaku confirmed last month that Ibrahimovic had given him his blessing to wear his old No9.
“Strikers play with No.9,” he told ESPN.
“It’s a nice number, and I asked the permission of Zlatan Ibrahimovic.
“I want to thank him, as well, for allowing me to wear that number.”