The Swede was presented to the media this afternoon after putting pen to paper on a three-year contract. Milan are thought to have netted around 25m.
"I'm sorry for the wait," he said after days of talks with his agent. "I want to thank Paris Saint-Germain for the great work which they have done, for making the impossible possible.
"I'm happy, I'm finally a PSG player. I'm happy for the club, for the fans - it is an interesting project which I want to be part of. I now want to make history and win.
"I've come to a Dream Team. They have other great players, they've bought the best defender in the world - Thiago Silva [from Milan]. As long as he is behind me, I don't have to look back.
"Who doesn't want to be here? PSG will win trophies. This is the future."
"I'm very happy that I was at Milan," he said when asked about any possible problems at San Siro. "They gave me my smile back. I will always have great memories of Milan. They will remain in my heart.
"I wish Milan good luck with everything. They were successful before I joined them and they will continue to be successful.
"I gave Milan my best and I have nothing negative to say. I just have a positive vision.
"I said that my contract with Milan would be my last, but you never know what will happen in life. I don't want to think about the past, just the future.