The Spaniard is believed to have cost the Reds in the region of £6million.
Jose Enrique: "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.
"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.
"Everybody speaks about the fans here and they are amazing. I am looking forward to it. I am looking forward to playing in front of the Kop. I hope it will be this weekend, but if not I can wait."