The two clubs have finally been able to announce the deal after days of speculation, completing a much-talked-about move for the promising left-back.
"[Bramall] is a young, promising left back who has a lack of experience at the top level but who has fantastic ingredients," said Wenger, according to the club's official website.
"He has tremendous pace, a good left foot, a great desire to do well. Overall, he's a very exciting prospect."
The deal comes after Bramall spent two days on trial with Arsenal, where he was invited to train with the senior squad.