Al Arabi have paid £39m to take the diminutive Italian midfielder away from the French champions.
The 30-year-old has signed a three-year contract with his new club.
Verratti joined PSG as a 19-year-old from Serie B side Pescara for €12m in the summer of 2012 and went on to make 416 appearances, which is the second most in the club's history.
Verratti won among others nine Ligue 1 titles and scored 11 goals, but the UEFA Champions League trophy proved elusive, coming closest in the 2020 final defeat to Bayern Munich.
"I was very proud to wear the colours of Paris St Germain for more than a decade, to rub shoulders with so many great players, and to win 30 trophies," Verratti told PSG's website.
"Paris, the Club and its supporters will always have a very special place in my heart. I will be Parisian forever."
"Marco will forever be linked to Paris Saint-Germain," said Paris Saint-Germain President Nasser Al-Khelaifi.
"He has always been there for the Club, giving his whole heart on the pitch and achieving so many great things with us."
Verratti has been capped 55 times by the Italy national team and helped the Azzurris win EURO 2020.
