The 25-year-old Real Madrid midfielder was part of the deal that involved Michael Owen going to Spain.
"Even if Owen hadn't signed for Madrid, I already had an offer from Liverpool and I knew that the manager was keen to sign me, which is something to be proud of," he said.
"Last season, I found out how hard it would be to play at Real and I know Liverpool will be the same, but I hope to get some more minutes on the pitch.
"It is never going to be satisfactory leaving the best team in the world, but playing for Liverpool is a dream come true for any player."
Nunez will wear the number 12 shirt, and may make his debut against Manchester City on Saturday.
