"I feel very pleased and proud," he said. "It feels like I'm signing for the first time - everything has changed so it's like a new beginning for me with new confidence and a new boss."
The 30-year-old left Anfield when his contract expired in May but was offered a chance to prove he was worth retaining by new manager Roy Hodgson and has agreed a deal until 2012.
"I asked the club to find out whether Fabio had found a new club," Hodgson told the Liverpool website.
"When we ascertained that he hadn't, we invited him back to (the training ground at) 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," he added.
Aurelio endured an injury-marred spell at Anfield after joining from Valencia in 2006 but said on Saturday he thought he was in good condition after training on his own in pre-season.
He was part of the squad that travelled to Germany for Sunday's pre-season friendly with Borussia Moenchengladbach.
