"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," Al-Khelafi told the club's official website.
"We are particularly pleased to welcome a young French player in our team."
Digne, who helped France win the Under-20 World Cup on Saturday, revealed his delight at joining the club.
"Playing at Paris Saint-Germain with exceptional players is a childhood dream and a great joy," said Digne.
"After becoming a world champion, I had a fantastic summer. I thank the club officials for their confidence."
The 19-year-old will wear the number 21 shirt for the club.