The former Lille standout has been courted all summer by the Ligue 1 champions and the clubs have now come to an agreement
The young Frenchman has long been linked with a move away from les Dogues, with the Parisians and Monaco both vying for his signature.
However, Laurent Blanc's men have won the race for the 19-year-old, who has signed on at the Parc des Princes.
Digne starred for the France U-20 side which won the World Cup in Turkey earlier this month following a victory over Uruguay in the final.
The left back will wear the number 21 for Les Rouge-et-Bleu, and Digne is deligted to be joining the Ligue 1 champions
"Playing at Paris Saint-Germain with exceptional players is a childhood dream and a great joy. After becoming a world champion, I had a fantastic summer. I thank the club officials for their confidence," Digne said.
The player has also been welcomed to the Parc des Princes by the club's chairman.
"Lucas Digne, one of the great hopes of French football, recent winner of the World Cup and less than 20 years old, courted by leading clubs, chooses Paris Saint-Germain to assert himself on the European stage. We are particularly pleased to welcome a young French player in our team," said Nasser Al-Khelaïfi, chairman of PSG.