The deal, which has the option of a third year, is subject to a medical.
The Argentina captain, 34, left Barca - the only club he has played for - as they could not afford a new deal under La Liga's financial fair play rules.
A PSG news conference will take place in the auditorium of the Parc des Princes on Wednesday at 10:00 BST.
Mauricio Pochettino's PSG finished second to Lille in Ligue 1 last season.