Before his 18 month stay in Russia, Paredes played at Roma and Boca Juniors.
"I'm very proud to be joining Paris Saint-Germain," he said. "After my experiences in Italy and Russia, I'm looking forward to this fantastic opportunity to join one of the most prestigious clubs in the world.
"For someone who grew up in the passion of Argentine football, I'm keen to savour the atmosphere at the Parc des Princes."
Thomas Tuchel, the PSG boss, has long been agitating for a high quality midfielder to join the ranks.
That desire has been heightened by the row between the club and Adrien Rabiot who has been distanced from the first team after refusing to sign a new contract. Injuries to Neymar and Marco Verratti have compounded Tuchel's dismay.
Defenders Dani Alves and Marquinhos have been pushed into midfield in the absence of the two stars. The recruitment of Parades should allow one of the two to revert to more accustomed duties.
"We're happy to welcome Leandro at PSG," said club president Nasser Al-Khelaïfi.
"He has all the traditional qualities of Argentine football - fighting spirit and technical quality. I'm sure he will fit quickly into the team."
PSG, who are 13 points clear of second placed Lille, are seeking a fifth French title in six years. The side is also into the quarter-final of the French Cup as well as the knockout stages of the Uefa Champions League.
PSG travel to Old Trafford on 12 February for the first leg of their last 16 clash against Manchester United.