The former Brazil international will leave the Parc des Princes club at the end of the current transfer window in August.
Leonardo saw his touchline suspension extended last week until June 30, 2014, after an appeal against an initial ban for shoving referee Alexandre Castro after a game against Valenciennes last season.
The 43-year-old was brought to the ambitious French club by the owners, the Qatar Investment Authority, in July 2011.
But the French champions have accepted Leonardo's resignation on Wednesday with "regret" and thanked him for his contribution to the club over the last two years.
Leonardo today informed Paris Saint-Germain of his desire to resign from his position as sport director at the end of the current transfer window.
We regret his choice but respect his decision. 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.
Leonardo was the spearhead behind a major spending spree at PSG and was also responsible for the appointment of Carlo Ancelotti as head coach at the club in December 2011 to replace Antoine Kombouaré.
Leonardo embarked on an ambitious transfer plan with high-quality players such as Zlatan Ibrahimovic, Thiago Silva and Salvatore Sirigu arriving in the French capital, while others such as Lucas Moura and Marco Verratti also proved invaluable as the team secured their first title since 1994 this year.
The Brazilian was also instrumental in helping to secure the services of David Beckham on a short-term basis for the second half of last season.
However, Leonardo was a controversial figure at times for the French club. His shove on match official Castro in May initially earned him a nine-month suspension by the French Football League, as Peter Mason of the Guardian reported, while PSG was handed a suspended three-point deduction.
Ancelotti left PSG last month for Real Madrid and was replaced by former France international Laurent Blanc.