Brown, who leaves following the relegation of the club from the Football League, has said that he hopes Barnet can return to League Two as quickly as possible.
"I really enjoyed my time at Barnet," he told the club's official website. "From the moment I came in with Robbo (Mark Robson) I was made to feel welcome and that has been the case throughout my time at the club.
"It would have been nice if things had turned out differently on the pitch but I wish everyone at the club the best and hope they have a speedy return to League Two."
The Bees were relegated from League Two on goal difference.