Brown has also managed Derby County, Preston North End and did a caretaker stint at Bolton Wanderers, but is best known for coaching Hull to promotion to the Premier League in 2008.
Brown is set to be in charge of Southend for the first time when they face Fleetwood Town on Monday.
But sacked manager Paul Sturrock will take charge of the club for one last time in the Johnstone's Paint Trophy final against Crewe on April 7 as a reward for leading them to Wembley.
Sturrock was given the chop with Southend ninth in League Two, six points behind Rotherham United. Under the Scot, they reached the League Two play-offs last season, but failed to win promotion to League One.
"I’m delighted to have been given the opportunity here at Southend and it’s a challenge I’m really looking forward to," said Brown.
“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.”