The Gunners signed the Dutch defender, 22, on Friday for an initial £34million, with £4m in add-ons, on a five-year contract.
“It was because of my brothers,” he told the club website. “They were always Arsenal fans, and I just loved seeing Arsenal play.
“They had big players, the way they played, the style. I just love the club.
“I had this from a young age, but my brothers kind of put that in me. I liked watching Robin van Persie of course, and Thierry Henry. They were my favourite players.”
Mikel Arteta is set to deploy Timber as a right-back in competition with Ben White when he sets out on the club’s tour of the United States this weekend.
But the new signing is confident he can pitch in at a number of positions.
“I think that I'm lucky to say that I can play as a central defender, as a right full-back, sometimes even in midfield,” he added.
“So I think that's a good thing and I need to keep that.
“I just like the way Arsenal play, is a bit similar to Ajax’s style and I like to play from the back. I can see a lot of similarities, especially in the way Arsenal and Ajax want to play.”