The Brazilian has parted company with the Reds after six years at Anfield and is on his way back to Porto Alegre after agreeing a one-and-a-half year deal with the Tricolor
The left-back, who had been at Anfield for six seasons, has put pen to paper on a contract with the Tricolor that will keep him in Porto Alegre until December 2013.
Aurelio joined Liverpool from Valencia in 2006 but the 32-year-old Brazilian's time at Anfield was blighted by injuries and he made just 86 appearances for the Premier League outfit.
The Brazilian looked set to part company with the Reds in 2010 when his previous contract with the club expired that summer. However, Aurelio was subsequently re-signed by Rafa Benitez's successor, Roy Hodgson.