The former England captain, a free agent since leaving LA Galaxy in December, joins the Ligue 1 leaders on a five-month contract.
Beckham considered offers from around the world but has opted for a club in the knockout stages of the Champions League, backed by wealthy Qatari owners and led by Carlo Ancelotti, who was manager at Milan during his first loan spell there.
Addressing the press at his official unveiling, Beckham said: "I'm excited. it's something we've been talking about for quite a while and it's finally happened.
"I'm very lucky. I'm 37 years old and I had more offers now than I've had in my career. I chose Paris because I can see what the club are trying to do.
"It's an exciting city, but now there's a club that's going to have a lot of success over the next 10, 15, 20 years. To be part of something that's growing is something that's very exciting to me."
Beckham confirmed he had offers from England but said: "Unless it was Manchester United I wouldn't want to play for a Premier League team."
And on the prospect of a reunion with Ancelotti he said: "Carlo's one of the best managers I've worked with."
England manager Roy Hodgson believes the move to PSG is "fantastic" for Beckham.
"David is a footballing icon, not only in this country but all over the world," he said. "He is one of the most recognisable footballers anywhere.
"We are perfectly aware of who he is, what he is and what he has done. All I can do is wish him all the best.
"Let's hope he can be as big a success at PSG as he has been everywhere else."
France boss Didier Deschamps believes Beckham's arrival will provide a welcome boost for the profile of Ligue 1.
"He's a personality who goes beyond football, like Zlatan Ibrahimovic maybe. They are players who beyond our frontiers give an important visibility to Ligue 1.
"But I won't judge it on a sporting perspective. I'm not the coach, general manager or owner of Paris St Germain. They've made their choice with David Beckham. He's a world football personality."