Mbappe was a top target for the Gunners, who failed to qualify for the Champions League after finishing fifth in the Premier League last season.
"Yes, I met with Arsene Wenger, who is a great coach," Mbappe said. "He has a great reputation here in France, he's well-respected and knows how to develop young players.
"This was a real option for me. But, of course, Paris Saint-Germain was the main option. We weighed up the advantages and disadvantages of all the clubs but my family told me it had to be my decision and one I needed to make.
"It also had to be a long-term decision. So it was up to me and I decided to come here in order to develop."
Mbappe has some experience of English football from earlier in his career, having had a trial at Chelsea well before turning professional, when he met fellow Francophone players Didier Drogba and Florent Malouda.
"It was a wonderful experience. Chelsea was the first great club, the first big club, that I went to visit. So it was a real discovery for me," Mbappe said. "I was coming from my grass roots, amateur club. It was a whole new world.
"Of course I had an idea what a great football club was like but I was really impressed by the working culture and the mentality of wanting to be better day-in, day-out and visiting this infrastructure helped me, actually, with my development.
"I saw things differently because up until then I had just a French mentality and after that I could pick what was positive in other mentalities and build my own.
"I got to meet some of the first-team players - Drogba, Malouda – the French-speaking ones and took some pictures with them.
"An idea has been reinforced since I was a kid – not just because I went to Chelsea. I always thought: 'I want to be there, I want to be one of those big players who is trying to give people fun out of the game.'"