Alex reunited with Ancelotti at PSG
"I had a problem with the [Chelsea] coach [Andres Villas Boas], he doesn't like my football. I preferred to leave for another club," Alex told a news conference shown on PSG's website.
Alex, 29, joined Chelsea from Santos in 2004. He was loaned to PSV Eindhoven from 2004 to 2007.
"He has a lot of experience because he played in the Dutch and English leagues and also with his national team," coach Carlo Ancelotti, who took over from Antoine Kombouare last month and managed Alex at Chelsea, said.
"He is a great professional. I think he will have a good season."
Alex is PSG's second major signing during the January transfer window after full-back Maxwell joined from Barcelona.
Qatar-backed PSG, who spent more than 80 million euros last summer, have yet to buy a major striker, having failed to sign Alexandre Pato from AC Milan and Carlos Tevez from Manchester City.
Ancelotti is unconcerned, however, as PSG are not involved in the Champions League.
"When you play the Champions League you need four strikers. But to play the league and the Cup, [Kevin] Gameiro and [Guillaume] Hoarau are enough," the former Chelsea manager said.
PSG director of football Leonardo said that Alex's arrival was effectively shutting the door to Manchester City striker Carlos Tevez as the club have already a maximum of four non UE players.
"But who knows in the future," he said.