The Ivory Coast international, previously close to Arsenal, underwent a series of physical tests early on Wednesday ahead of his proposed switch to the Ligue 1 champions
The Ivorian right-back had previously been the subject of an approach from Arsenal as they sought a replacement for Bacary Sagna, who has joined Manchester City, but the Gunners began considering alternative options in May.
The Premier League side eventually opted to sign Mathieu Debuchy from Newcastle, allowing PSG to steal a march on the signing of the 21-year-old, who is expected to cost up to €10 million (£7.9m).
With Chistophe Jallet set to leave the Ligue 1 champions, Laurent Blanc was keen to add a new defender to their squad to fight it out with Gregory van der Wiel for the position of right-back.
Aurier came through the ranks of the Lens youth academy and joined Toulouse in the summer of 2012. He had since developed into a key player at the Stadium Municipal, making close to 100 official appearances.
The defender was part of the Ivory Coast World Cup squad who exited at the group stages and impressed in the 2-1 win over Japan as he set up both of his side's goals.