The 34-year-old Hartlepool born midfielder, who was a free agent after leaving Pompey, has agreed a one-year deal at Elland Road.
Simon Grayson told the official club website: "He has experience and know-how, and he has played at the highest level.
"He is a player that I have long been interested in and I'm glad we've been able to sort it for him to come here."
Brown has 524 appearances to his name since starting his career in the youth scheme at Manchester City and has also had spells at Sheffield United, Tottenham Hotspur, Fulham and Wigan.
He becomes Leeds' second signing of the summer, following the arrival of former Blackpool goalkeeper Paul Rachubka.
Brown made his debut for Manchester City in August 1995 against Q.P.R. in which he was actually sent off after only 10 minutes after coming on as a substitute. A sign of things to come from the tough-tackling midfielder!