Brown led Hull to the Premier League in 2008 and kept the club in the top flight before being placed on gardening leave the following season, which ended in relegation.
An unsuccessful spell at Preston North End followed for Brown before he took charge of League Two Southend in March 2013.
The 54-year-old will now welcome Hull, who are back among England's elite clubs under Steve Bruce, to Roots Hall on January 25 or 26.
"You couldn't write the script; it really is what the FA Cup is all about," Brown told Southend's official website.
"It's a great draw for me personally coming up against Hull, but also for the players to test themselves against a Premier League side.
"We've beaten two teams from our division (Morecambe and Chesterfield), two good teams, and then convincingly beaten a Championship side (recording a 4-1 triumph over Millwall), so we deserve a crack at Hull.
"One of my ambitions when I arrived at Southend United was to fill the stadium and I think we can do that against Hull.
"I know Steve Bruce very well - we get on - and he's got a good team together, so it'll be a cracking FA Cup tie.
"It's also nice to have the draw at home. If we’re going to try and go further in this competition, I felt it was important we were at home.
"There's two big games before then (in League Two) which the players need to focus on, but it's a game we can all look forward to in the near future."
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