The powerful, attack-minded left-back has been a central figure in Tony Carr's side over the past two seasons, making 45 FA Premier Academy League and FA Youth Cup appearances since his debut in a home win over Millwall in January 2008.
Brown is a cousin of Sunderland and England midfielder Kieran Richardson, who he shared a pitch with for the first time during Carr's testimonial.
"It's been a long time coming, but now I've signed my first contract it has made all the hard work worthwhile and is a good start," Brown told whufc.com.
"It hasn't really sunk in yet, but it's the best news I've heard. This is what I've always wanted to do. I've been confident the whole way through and have always worked hard to pursue my dream. I've seen loads of boys come and go, some of whom were really good players, so to come through is something special."