Arsenal chief scout Steve Rowley had run the rule over the starlet dozens of times and Wenger immediately sanctioned the signing.
Wenger said: "It was my scout who alerted me to him.
"I watched him in one game against Ipswich in the Youth Cup final and I liked some things about him and that convinced me.
"We watched him 50 times beforehand, sending scouts. But I have to be convinced about players, too.
"What convinced me was the timing of his runs. That is the first quality - to know when to go and where to go.
"Sometimes you have players who are super-quick but they don't run at the right moment and they don't use their asset very well.
"Every player who comes to Arsenal makes the right choice."
The Gunners manager described how Walcott has come on in leaps and bounds since he joined the north London outfit.
He continued: "Theo has become more of a man and more mature in his game. He has developed his link play, his first touch, his commitment. But that's normal, from 17 to 19 and there is still a lot to come from 19 to 23.
"You become a real man but at 19 you are still a boy.
"He has been in the first team and he has done well.
"Since the beginning of the season, he has been playing regularly - and it shows in terms of development."