The 20-year-old failed to make a first-team appearance for the Hammers during his rise through the ranks at Upton Park but did enjoy time at Aldershot and Crewe on loan last season.
And Bees Head Coach Mark Robson has welcomed Brown to his ranks having fought off competition from rival clubs for his signature.
Robson told Barnet's official website: "Jordan is a player I've known about for a while now. He's had a good upbringing at West Ham - both on and off the pitch.
"He is a very promising player and was unfortunate not to feature more in the West Ham first team as he played a few times in pre-season last year. With all the players they brought in he never really got an opportunity.
"But that can only be a good thing for us as I really want to help him develop and prosper as a Bee and I believe he will do that here."