Brown takes over the reins at Roots Hall from Paul Sturrock who departed the League Two club on Sunday.
The 53-year-old, who has been out of work since leaving Preston in December 2011, met the Southend players at the club's training ground on Monday morning before agreeing terms.
Brown has also managed at Derby and Hull City, who he guided to promotion to the Premier League, as well as a spell as caretaker manager at Bolton.
His first match in charge will be at Bradford City on Good Friday as he bids to revive the Shrimpers' play-off fortunes - they have six points to make up on seventh-placed Rotherham in their remaining seven games.
Brown told the club's official website: "I'm delighted to have been given the opportunity here at Southend and it's a challenge I'm really looking forward to.
"We've got seven league games between now and the end of the season, hopefully we can put a winning run together and give ourselves a chance of reaching the play-offs.
"We've got a few days of training between now and the game against Bradford that will give me a chance to take a look at the players.
"The Easter period is always tough because you play twice in such a short space of time, but it's a good opportunity to pick up six points and get that winning run started."
Southend have confirmed that Sturrock will return to lead the side out at Wembley for their Johnstone's Paint Trophy final against Crewe on April 7.