The forward, speaking at a news conference on Monday alongside PSG president Nasser Al-Khelaifi, also denied that his desire to exert a greater influence off the field had been a part of discussions, and left the door open to a possible departure in 2025.
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PSG announced Saturday -- ahead of their last game of the season against Metz at the Parc des Princes -- that Mbappe would be signing a new deal, bringing an end to one of the most high-profile transfer sagas of recent years.
"Everybody knows I wanted to leave last year. But things are different now, in sporting terms and personally," Mbappe said. "Leaving my country wasn't the right thing. There's a sentimental aspect to this, and the sporting project has changed as well. ... We spoke for months about the sporting project, and we spoke about money for just a few minutes."
On Saturday, sources told ESPN that the 23-year-old had personally contacted Madrid president Florentino Perez to reveal his U-turn after days of uncertainty around his future.
"I made my decision last week," Mbappe said. "I spoke to Florentino Perez. I have a lot of respect for him and for Real Madrid. They did everything to bring me there and make me happy, so I thank them for that."
Mbappe has been a long-term Madrid target, coming close to joining the club several times, including last summer, when they made a series of bids worth up to €200 million, hoping to take advantage of his contractual situation.
Madrid stayed in touch with Mbappe's camp throughout this season and believed they had the player's word that he would join them when his contract expired on June 30.
The forward denied that PSG offered him the club captaincy -- as well as input on transfer policy and other key decisions -- to persuade him to stay in Paris.
"I'm not going to go beyond my role as a player," he added. "You don't need special responsibility to be involved in this project. There's a captain at this club, Marquinhos, and I'm not looking to take over from him. I don't need to be captain to give my point of view."
Mbappe -- who was born and grew up in Paris -- has been at PSG for five years, becoming the club's second-highest scorer of all time with 171 goals, including a hat-trick in Saturday's 5-0 win over Metz.
However, when asked Monday whether he expected to remain at the club beyond 2025, Mbappe refused to rule out a move away.
"Something I've learnt in football is you should look ahead, but not too far ahead," he said. "A year ago I didn't think I'd be sitting here, and now I've signed a new contract. ... I'm focusing on this new project. I don't know what will happen in the future. I don't know where I'll be in three years."