White, who spent nine years at Colchester before arriving at Roots Hall last month, has impressed the former Hull manager with his attitude during pre-season and will take the armband for the new term.
"John conducts himself well on and off the pitch and I think he will be a good captain for us," Brown told the Southend Echo.
"He's not afraid to get stuck in and he still has a black eye from when he did exactly that against Chelmsford City.
"It wasn't an easy decision to make because there were a lot of candidates to pick from, but I wanted to make it a Phil Brown Southend side by choosing someone who I signed."
The 26-year-old defender becomes the Shrimpers' third summer signing as Brown hopes to make a return to League One in his first full season in charge.