Aurelio left the Reds when his contract expired at the end of May after rejecting a pay-as-you-play deal at Anfield.
New Liverpool manager Roy Hodgson has now decided to re-sign Aurelio.
“I asked the club to find out whether Fabio had found a new club,” Hodgson told the club’s official website.
“When we ascertained that he hadn’t, we invited him back to Melwood so both myself and my staff, and the medical team could properly assess the player.
“We were both very impressed and I am delighted we were able to re-sign Fabio.”