PSG secured Messi's signature after the forward had failed to agree fresh terms with Barcelona, who are enduring financial difficulties amid complications with LaLiga.
The 34-year-old moves to the Parc des Princes having scored 672 times in 778 appearances for his former club and furthers PSG's already remarkable depth of attacking talent.
After confirming Messi's arrival on Tuesday, Al-Khelaifi said: "I am delighted that Lionel Messi has chosen to join Paris Saint-Germain and we are proud to welcome him and his family to Paris.
"He has made no secret of his desire to continue competing at the very highest level and winning trophies, and naturally our ambition as a club is to do the same.
"The addition of Leo to our world class squad continues a very strategic and successful transfer window for the club. Led by our outstanding coach and his staff, I look forward to the team making history together for our fans all around the world."
Messi joins former colleague Neymar as he prepares to form a startling front three with the Brazil forward and France star Kylian Mbappe.
The signings of Sergio Ramos, Gianluigi Donnarumma and Georginio Wijnaldum alongside Achraf Hakimi strengthened Mauricio Pochettino's men, but Messi's historic move could take PSG to a new level.
Having been pipped to the Ligue 1 crown by Lille last term, PSG started their quest to reclaim the title with a 2-1 win at Troyes on Saturday and will hope the addition of Messi can inspire them to a first Champions League success.
Messi has won four Champions League titles with Barcelona alongside 10 LaLiga triumphs.
The forward also guided Argentina to their first Copa America success since 1993, scoring four goals as he sealed his first senior international trophy in July.