The 25-year-old has become Liverpool's fifth major signing so far this summer.
He told Liverpool's official website: "This is one of the happiest days of my life. I have come to one of the biggest clubs not just in England, but in the world. I am really, really happy.
"They have won a lot of things including the Champions League. They have amazing players and I hope to win things here.
"Of course I am looking forward to playing in front of the Kop. Everybody speaks about the fans here and they are amazing. I am looking forward to it. I hope it will be this weekend, but if not I can wait."
He added: "Damien Comolli told me it is an amazing club. In Spain there is a saying, 'When the train comes in, you have to take it.' This is the first time a big club has come in for me and I had to take it (the opportunity). I am really happy."
Enrique insists he is ready to feature in the Premier League season opener against Sunderland in just a little more than 24 hours.
"If the manager needs me, I am ready to play," said Enrique. "I have already played for Newcastle in pre-season, not every game but two or three games and I am fit and if the manager needs me, I am ready to play.
"My ambition is win everything with Liverpool. This year we won't play in the Champions League, so the most important thing is to try and win the league."