"I'm very proud to be joining Paris Saint-Germain," Paredes told PSG's official website. "I now have this fantastic opportunity, not only to discover a new league, but... to wear one the most prestigious club jerseys in the world."
PSG chairman Nasser Al-Khelaifi said Paredes would bring guile and strength to the club's midfield.
"Leandro brings with him the traditional strengths of Argentinian football, a fighting spirit and excellent technical skills," he said. "I am sure he will fit quickly into our coach's well-organised and ambitious team."
The French champions, who have a 13-point lead at the top of Ligue 1, travel to third-placed Lyon on Sunday.
(Reporting by Rohith Nair in Bengaluru; Editing by Amlan Chakraborty)