The Nancy keeper will remain at his current club for another season to allow him to develop further before making the move to the runner's up of Ligue One.
It was confirmed by Monaco's official website that the 20 year-old had signed a five year deal with the club for a fee of around 3 million euros.
Monaco vice president Vadim Vasilyev spoke of Nardi very highly upon signing. "Paul Nardi is one of the great hopes of French football. He enters our strategy to build a long term vision, we are delighted that he has selected our project as we faced competition from other European clubs."
"To allow him to continue his progression, Paul will be loaned to Nancy next season."
The youngster made 33 appearances for the Ligue two side last season and almost helped them to promotion to France's top flight.