The 23-year-old forward becomes the fifth summer acquisition made by Unai Emery's side following the arrivals of Hatem Ben Arfa, Grzegorz Krychowiak, Thomas Meunier and Giovani Lo Celso.
"I am delighted to join Paris Saint-Germain, who have become one of Europe’s most competitive clubs," Rodriguez told his new club's official website.
"Like Paris Saint-Germain, I have big ambitions for the coming seasons and it will be a great pleasure to work under the direction of Unai Emery, who has developed an excellent reputation in Spain, and across Europe, for his quality as a coach. I can't wait to begin this next challenge of my career."
The former Spain youth international won two Champions League crowns, one La Liga title and the Copa del Rey during a five-year stay at the Santiago Bernabeu.
PSG president Nasser Al-Khelaifi added: "I am very happy to welcome Jese to PSG. Over the past seasons, he has confirmed his status as one of Real Madrid's, and Spain's, most promising young footballers.
"After playing alongside some great forwards, he has chosen to continue his progression with Paris. His speed and creative qualities will complement our excellent attacking players.
"With Jese, our squad is now, more than ever, armed to confront the coming challenges and meet the expectations of our fans."