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.
Messi and his family were pictured at Barcelona’s El Prat airport on Tuesday afternoon after news of the deal emerged.
When asked by reporters whether his son would be joining PSG, Jorge Messi answered “yes”.
Considered one of the greatest players of all time, Messi scored a record 672 goals in 778 games for Barca, the club he joined as a 13-year-old.
He won the Ballon d’Or a record six times and lifted 35 trophies with the Catalan club.
The signing of Messi – who would be reunited with former Barca team-mate Neymar at the Parc des Princes – is one of the most noteworthy captures in football’s history.
He will play in a front three alongside the two most expensive players of all time – Neymar and Kylian Mbappe.
Unless there are any late hitches, he will become PSG’s fourth free-transfer signing this summer after the arrivals of Netherlands midfielder Georginio Wijnaldum, Spain defender Sergio Ramos and Italy goalkeeper Gianluigi Donnarumma.
Highly rated Morocco right-back Achraf Hakimi also joined from Inter Milan.
PSG are yet to win the Champions League in a decade of Qatari ownership and subsequent heavy investment, with the 2020 final defeat against Bayern Munich the closest they have come.
If the deal goes through quickly, he could make his PSG debut at home to Strasbourg on Saturday.
-BBC