The deal is subject to a medical.
The 34-year-old Argentina captain left Barca – the only club he has ever played for – as they were unable to afford a new deal under La Liga’s financial fair play rules.
Mauricio Pochettino’s PSG finished second to Lille in Ligue 1 last season.
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.
Unless there are any late hitches, he will become PSG’s fourth free-transfer signing this summer after the arrivals of midfielder Georginio Wijnaldum, defender Sergio Ramos and goalkeeper Gianluigi Donnarumma.
Highly rated right-back Achraf Hakimi also joined from Inter Milan.