Liverpool said the fee would remain undisclosed, but it is thought to be close to 30 million pounds.
The 27-year-old Alonso had been an integral part of the Liverpool side since joining in August 2004 from Real Sociedad.
He helped them to win the Champions League in 2005 and was instrumental in their push last season to second place in the league.
Liverpool manager Rafa Benitez had wanted Alonso to stay, but the midfielder's desire to join Madrid eventually persuaded him to allow him to leave.