The Uruguayan striker made his move before the transfer window closed on monday evening, and is looking forward to playing for the Reds.
"I want to show the fans how hard I am ready to work," said the 24-year-old. "I want to put a lot of effort in to show my capabilities.
"I want to try to play as many games as possible and help move us up the table.
"My ambitions for the future are to do my very best for Liverpool, to try to learn more about English football and become a champion.
"Liverpool is a very famous club - the most famous in England and I watched Liverpool and English football as a boy. It's a dream to be able to come and play here."
