Sports daily L'Equipe and Le Parisien said that Beckham would join PSG in the January transfer window.
"It's done, Beckham has kept his word, he'll wear PSG colours for a year and a half," Le Parisien reported in a front-page story.
According to Le Parisien, the former England captain Beckham will become the top paid footballer in France, with a gross monthly salary of 800,000 euros (1 million dollars).
Bar a last-minute hiccup he was expected to sign a contract "in the coming days."
L'Equipe said the club was preparing a rockstar welcome for the 36-year-old player and his wife, Victoria.
A spokesman for Beckham told Sky Sports that the former England captain is "still weighing his options" what to do once his five-year contract at Major League Soccer champions Los Angeles Galaxy expires at the end of the year.
Beckham, who so far has only ruled out a return to England, has been linked with a move to Qatari-owned and ambitious PSG for weeks. He has reportedly also been offered a contract extension at the Galaxy.