The 34-year-old was accompanied by his wife and three children as he entered El Prat airport just before 1:30 pm (1130 GMT).
His father Jorge, who is also his representative, arrived a short while earlier.
Asked by reporters if his son would sign for the French club, Jorge Messi said: "Yes".
PSG have spent the last few days trying to finalise an agreement to sign Messi following his departure from Barcelona, the club he has represented for the entirety of his 17-year professional career so far.
The French side's supporters began gathering on Monday outside the club's Parc des Princes home and at Le Bourget airport to the north of the city hoping to catch a glimpse of Messi.
Reports in Spain during the night talked of a "final offer" by Barcelona to try to keep the player at the club.
Instead, the mooted move to Paris is on the verge of being completed as PSG prepare to add the six-time Ballon d'Or winner to an attack already featuring Neymar and Kylian Mbappe.
PSG see Messi as the missing piece in their jigsaw as they chase the Champions League, the trophy they want more than anything else.
"I am happy if he arrives in Paris," new PSG goalkeeper Gianluigi Donnarumma told Sky Sports Italia on Monday outside his Parisian hotel.
"He is the strongest in the world, I am excited and happy at the thought of having him in the team."
For an optimal experience, please
