كتب : Amro Hassan
The 31-year-old, who recently won the FIFA Confederations Cup with Brazil, has earlier revealed his intention to leave Allianz Arena.
"Lucio agreed to end the contract running until 30 June 2010," read a statement on Bayern's official website.
"He now moves with immediate effect to the Italian champions Inter where he will sign a three-year deal."
Lucio joined Bayern in 2004 coming from other Bundesliga side Bayer Leverkusen.
The former Internacional player won three league titles and three cup trophies during his stint with the Bavarians.