Laurent Blanc's men added to last season's domestic treble with a 2-0 win over Lyon in the Trophee des Champions in Montreal on Saturday.
The Ligue 1 side also beat the likes of Manchester United, Barcelona and Chelsea to the International Champions Cup in their pre-season tour of the United States.
And Al-Khelaifi is confident the team will add more titles over the coming years and begin to challenge the likes of Barcelona, Real Madrid and Bayern Munich in the Champions League.
"Once again, I am a proud and happy president of Paris Saint-Germain," he said of their latest trophy win. "I congratulate the players and the staff for this victory - our third in a row.
"It is a reward for the tremendous work done by the players and staff during preseason, which was also marked by our victory in the International Champions Cup against our leading European rivals.
"These victories confirm this success and all our ambitions remain the same: to win all possible titles in France and continue to grow in Europe."
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