The 24-year-old, who is primarily a left-back, had been without a team since leaving Colchester United in February.
Brown told the club's official website: "He's done really well since he's come in on trial and really put a marker down.
"He has worked extremely hard and I think him and Anthony Straker are starting to form quite a nice partnership on the left-hand side.
"Having Ben sign gives us options as Straker can drop back if needed or Chris Barker can move to left-back. I'm delighted to have signed Ben and I'm sure he'll do very well."
Brown has featured in all of Southend's pre-season fixtures to date.