He has signed a one-year deal with an option for a further year worth £200,000 a week. He revealed that United was to be his next destination on social media on Thursday in a move which stunned Old Trafford officials, who were still to agree terms.
But 24 hours later it was, with with manager Jose Mourinho hailing the new arrival as 'one of the best strikers in the world'.
And a delighted Ibrahimovic, 34, said: 'I cannot wait to work with Jose Mourinho once again.
'He is a fantastic manager and I am ready for this new and exciting challenge. The only regret I had with Jose was that I had a short time with him. I had one season (at Inter Milan). We won together, we enjoyed it together and had a great time together.
'I learned a lot and I got to know him as a person, not only as a coach, and only positive things.
'He's a winner, I'm a winner and we both know what we want. We want to win. Wherever we go, we win. And we will win.'
Mourinho said: 'Zlatan needs no introduction. The statistics speak for themselves. Ibra is one of the best strikers in the world and a player who always gives 100 per cent.
'He has won the most important leagues in the world of football.
'Now he has the opportunity to play in the best league in the world. I know he will grasp this opportunity and will work hard to help the team win titles.'
Ibrahimovic scored 156 goals in 180 appearances for PSG. He added: 'I'm super excited, super, super happy. Finally it's done.
'There's been a lot of talks, but it came to the moment where everything is done, and now we start. Now the hard work starts, so I'm super happy.
'I'm just waiting to get to know the guys at the first training. It looks like it is a big club, a huge club, so I'm excited.
'I'm happy, now I can focus on one thing and that's the United shirt.
'My decision was pretty easy. It was more to make it possible, everything. I compare it with the Mayweather and Pacquiao fight - they said it would never happen but it happened.
'If I could win here... I don't know how many players have had the possibility to play in different competitions like I have and at the same time be winning.'