The French champions announced the news on their website and Leonardo will leave Paris when the current transfer window closes at the beginning of September.
The Brazilian was recently banned for the whole of next season for shoving a referee after a game against Valenciennes in May.
A PSG statement read: "We regret his choice but respect his decision."
Leonardo was appointed by PSG's Qatari owners in 2011, and his recruitment policy has played a key role in re-establishing the club as a force in European football.
PSG's statement went on: "We thank him greatly for his important contributions towards the project of building a top European club in Paris and wish him all the best for his future career choice."
Laurent Blanc was named PSG manager last month following the departure of Carlo Ancelotti, who had previously worked alongside Leonardo at Milan.
During Leonardo's time at Parc des Princes, PSG signed the likes of Zlatan Ibrahimovic, Marco Verratti, Ezequiel Lavezzi, Lucas Moura, Javier Pastore, Thiago Motta and David Beckham - with the Ligue 1 title duly following last season.
Leonardo was also key to the appointment of Ancelotti as head coach, although the Italian has since left to take charge of Real Madrid.
His influence over new manager Blanc was always likely to be diluted by the increased ban he received from the French Football Federation (FFF) for allegedly pushing referee Alexandre Castro following a match against Valenciennes on May 5.
Leonardo was initially handed a nine-month ban but, after a failed appeal, it was increased last week to expire on June 30, 2014, during which time he could not be present on the touchline or enter referees' dressing rooms.
PSG have stood by Leonardo throughout, reaffirming their confidence in him and issuing a statement in which they said they "deplored the severity of the new, harsher penalty".
The club announced they would explore future legal options once they had received and studied the wording of the FFF's decision, but those plans are now set to be shelved in the wake of today's announcement.