The six-time World Player of the Year is a free agent after Barcelona announced they were unable to fulfil the terms of a new contract due to financial difficulties.
The 34-year-old bade an emotional farewell to the Catalan club at a press conference at the weekend.
PSG were immediately linked with the Argentine and several reports in Spain and France say he has agreed a two-year deal with the Parisians.
Messi arrived at Barcelona airport on Tuesday morning shortly after his father and agent Jorge. They flew to Paris to complete his medical.
While Messi was preparing to depart at the airport his imagery on the side of Barcelona's Camp Nou ground was being taken down, a final reminder that one of the most trophy-laden partnerships in the history of world football was ending.
Barring any last-minute hitches, Messi will be reunited with former Barca teammate Neymar and young France striker Kylian Mbappe in what would be one of the most feared attacking troikas on the planet.
Messi had remained in Barcelona on Monday where "devastated" supporters gathered outside his home on the hills of the wealthy Barcelona district of Castelldefels to catch a glimpse of their hero.
Messi has played his entire club career to date at Barca after joining the club at the age of 13.
He came close to leaving the club after a disagreement last summer but that was eventually resolved. His contract expired at the end of last season and despite agreeing a 50 per cent pay cut Barca were unable to finalise the deal due to the Spanish league's financial control rules and the club's debts, which total more than $1.2 billion.
He leaves Barca as their record goalscorer with 682 and having won 35 trophies.
Messi's impending arrival at Parc des Princes will be the fourth free transfer to Maurcio Pochettino's squad this summer following the arrivals of midfielder Georginio Wijnaldum, defender Sergio Ramos and goalkeeper Gianluigi Donnarumma.
Highly rated right-back Achraf Hakimi also joined from Inter Milan for a fee that could eventually cost €71 million.