The 31-year-old, who spent a year and a half with Liverpool from 2008, put pen-to-paper on a one-year deal on deadline day, marking his return to the English top flight.
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"My first game for Liverpool was against Sunderland, and I remember the stadium; the atmosphere was amazing," he told the club's official website.
"I’m very happy to come back to England, and now I can start to work with an Italian manager.
"I know his kind of football, his kind of work. He works hard, and tries to do his best on the pitch.
"The Premier League is the most beautiful league in the world. I left in 2010, but I was angry to leave this country, and now I’ve come back because I think I can do my best for Sunderland."