The 29-year-old has joined the French side for a transfer fee reported to be around €5million.
Alex has signed a two-and-a-half-year contract with PSG.
Chelsea confirmed the move on their website, saying: “Chelsea Football Club can confirm we have agreed terms for the permanent transfer of Alex to Paris St Germain.
“Everybody at Chelsea Football Club would like to express their thanks to Alex for his service and we wish him well for the future.”
