The 23-year-old completed his move to Pep Guardiola's side on Monday for a reported fee of £52million, making him the world's most expensive defender.
Mendy, who has signed a five-year deal at the Etihad Stadium, has been linked with City for several weeks and he admits that it is a move he has been desperate to make.
"I am very proud of it, this is what I wanted from the beginning," the France international, who is City's sixth signing of the transfer window, told the club's official website.
"As soon as the championship was over, I talked to my family and it was all clear in my head, I wanted to join Manchester City. I was really happy about it.
"I think I am the right person for the group. I adapt easily. There are some players with whom I exchanged a few emails, I knew them from years ago.
"It's good to be the sixth signing, that means they have excellent staff and are trying to reinforce it. It means Manchester City will have a competitive squad."
57 - Benjamin Mendy fired in 57 crosses from open play in the Champions League last season, more than any other player. Centred. pic.twitter.com/7hLru985lY— OptaJoe (@OptaJoe) July 22, 2017
The former Marseille man believes his attacking flair will be well suited to City and the Premier League.
"I can bring a lot of creativity to the game, I can offer different solutions, I like to play as a full-back and provide assists for the strikers," he said.
"I always considered the Premier League the best in Europe. I like the intensity, there's always an attacking mindset with a team like this one, who play with the ball.
"It's been a dream to play in the Premier League since I was a kid and I will do everything to enjoy it."
Mendy is also relishing the chance of working with Guardiola, adding: "He likes to motivate and push his players. He is in the same mould as Marcelo Bielsa, the same football family, and I think that can only be beneficial for us and the rest of the team."