The Ligue 1 club announced the transfer of the highly-rated 20-year-old on their official website on Friday for a fee thought to be in the region of £2.4million (€3million).
Monaco vice-president Vadim Vasilyev praised Nardi – who was recently voted the best goalkeeper of the Toulon Tournament – and confirmed that the stopper would be sent back to Nancy next season.
"Paul Nardi is one of the great hopes of French football. He enters our strategy to build with a long-term vision, we are delighted he has selected our project as we faced competition from other European clubs,” Vasilyev said.
“To allow him to continue his progression, Paul will be loaned [back] to Nancy next season.”
Nardi has come through the youth ranks at the Stade Marcel Picot and established himself as a first-team regular, starting 33 games for the Ligue 2 club last term.
With his side narrowly missing out on promotion into France’s top flight last season, Nardi admitted he felt privileged to be taken on by Monaco.
"I am very happy to join this great club that has a great vision for the future. I am honoured and impressed to be part of Monaco today,” Nardi said.
Nardi’s signing comes just a day after Monaco unveiled Leonardo Jardim as their new head coach on a two-year deal.