The 30-year-old has joined the Qatar Stars League side on a two-year contract until the summer of 2025, and PSG have reportedly received around €45m (£38.7m) for the midfielder's sale.
Verratti bids a fond farewell to the Parc des Princes after winning a staggering 30 major honours for Les Parisiens, who signed him for just €12m (£10.3m) in 2012.
While on the books at PSG, Verratti was hailed as one of Europe's most technically gifted midfielders, contributing 11 goals and 61 assists from 416 matches in all competitions.
The Italy international won nine Ligue 1 titles with the capital giants and claimed a runners-up medal in the 2019-20 Champions League, while played 38 times in the 2022-23 season.
However, Verratti's time at the Parc des Princes was also blighted by injuries, and he was informed this summer that he was not part of the club's plans moving forward.
Manuel Ugarte, Xavi Simons, Cher Ndour and Lee Kang-in were all added to PSG's midfield ranks over the summer window, while 17-year-old Warren Zaire-Emery has established himself as a regular starter for Luis Enrique.
As a result, Verratti was made surplus to requirements and did not make a single matchday squad for PSG before the international break, as Les Parisiens worked to finalise his exit.
"I've been very proud to play for Paris Saint-Germain for over a decade, to rub shoulders with so many great players and to win 30 trophies. Paris, the club and its fans will always hold a very special place in my heart. I'll forever be a Parisian," Verratti told the official PSG website upon his departure.
PSG president Nasser Al-Khelaifi also paid a moving tribute to the former Pescara youngster, adding: "Marco will be forever linked to Paris Saint-Germain, playing such a big part in our great history.
"I will never forget his arrival in 2012 at the age of nineteen. He has always been there for the Club ever since, giving all his heart on the pitch and achieving so many great things with us.
"I would like to sincerely thank Marco, and his family, on behalf of everyone connected to Paris Saint-Germain, he will always be part of the Club. We wish him all the very best with his new adventure."
PSG attacker Kylian Mbappe weighed in with his own commendation, posting on Instagram: "An exceptional player and person. Having the privilege of being by your side all these years has been an immense pleasure.
"Your time here will never be forgotten or neglected. One of the best players I have seen. Thank you my friend, I will miss you a lot."
In addition to his 30 team trophies, Verratti was named in the Ligue 1 Team of the Year in seven consecutive seasons between 2013 and 2019, while he was crowned the league's young player of the year in the 2013-14 campaign.