The 18-year-old joined the Paris outfit on a season-long loan from AS Monaco, with reports claiming there is an option to make the move permanent next season.
Mbappe, who scored 27 goals in 60 appearances for Monaco, believes PSG are a club that matches his ambition.
"It's a great day for me. First, I join Paris Saint-Germain, a great club where there is everything for me to improve, then I score my first goal with the national team," Mbappe told the club's official website.
"It could have been worse! Paris Saint-Germain is the ideal project to continue my progress.
"I'm an ambitious player and it's an ambitious club, so there is all we need to grow together and achieve great things.
"There are great players in Paris. All the right conditions come together to be able to enjoy myself and work hard. I have one match left with Les Bleus and then I can think about all that."