The 26-year-old left-back was signed from Malaga on deadline day for a rumoured fee of £8.3m after Gunners boss Arsene Wenger lost Kieran Gibbs to a thigh injury.
Monreal told the club's official website: "The Premier League is one of the strongest there is and everyone knows about it.
"It's a completely different way of playing to the Spanish League - it's a lot more physical, for example. As the days go by I'll get used to things and I'll give my all.
"Arsenal like to keep the ball, which is beneficial for me and I like this part of the team's game. I love playing with the ball at my feet, short, sharp touches, and good movement.
"I think Arsenal do have certain elements of Spanish football philosophy. The Spanish people know that there are players of great quality in this team and I hope we can play good football."
Wenger added: "We believe he can integrate our style of play and adapt very quickly to that.
"He has the characteristics to play our game because he is very mobile, has a good left foot and is very good in combination play. It is of course vital in our style of play."