Brown has joined the npower League Two club after previous spells in charge of Derby, Hull and Preston, with the Shrimpers currently six points off the play-off places with seven games to play.
Southend earlier confirmed Sturrock will return to lead the side out at Wembley for their Johnstone's Paint Trophy final against Crewe.
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."
Brown achieved promotion to the Premier League with Hull in 2008 but has been out of work since December 2011 following relegations with the Tigers in 2010 and Preston the following year.