The Red Devils confirmed the news of the 35-year-old's move, months on from being released by the Manchester club.
Ibrahimovic commented on the deal via his Twitter account:
It had been widely expected that Ibrahimovic would remain at Old Trafford past the end of the 2016-17 season given how impactful he had been in his debut campaign, netting 28 goals in 46 appearances in all competitions.
However, an offer of a one-year contract extension with the Red Devils was withdrawn after he picked up a cruciate ligament injury that kept him out of the end of last season, per Simon Mullock in the Mirror.
Manchester United have taken something of a risk signing Ibrahimovic, as he still has some way to go in his recovery and there is no guarantee he will ever return to his best.
The former Paris Saint-Germain forward proved with United last season, though, that his advancing years have done little to impact his sharpness.
After signing for United, it was predicted by some that he would not be able to produce the goods in the Premier League, per the Times' Tony Cascarino.
However, as the Swede had done previously at Paris Saint-Germain, AC Milan, Barcelona, Inter Milan, Juventus and Ajax, he scored goals, and Manchester United will be banking on him repeating the trick at Old Trafford.
United manager Jose Mourinho hinted at the potential re-signing of Ibrahimovic earlier this month, per The Independent's Jack Austin.
The Portuguese knows how deadly Ibrahimovic can be in front of goal and will be confident he can reproduce his clinical form of last term, when he was United's only reliable goalscorer, netting 17 in 28 appearances in the Premier League.
The talismanic forward will likely have to accept a slightly more limited role at Old Trafford for his second spell at the club. United spent £75 million on Romelu Lukaku in the summer, and the Belgian is now the No. 1 striker.
But Ibrahimovic could still be a huge asset, as his finishing has not deserted him, and he is one of the most experienced players in the game.