The Premier League sides had agreed a fee on Thursday although neither disclosed the sum involved with British media estimating it was around 6 million pounds.
"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," Enrique told liverpoolfc.tv.
The 25-year-old, who joined Newcastle from Villarreal in 2007, arrives on the eve of Liverpool's Premier League opener against Sunderland at Anfield.
"I am looking forward to playing in front of the Kop," he said. "I hope it will be this weekend, but if not I can wait."
Enrique was manager Kenny Dalglish's fifth major signing of the close-season after Jordan Henderson, Charlie Adam, Alexander Doni and Stewart Downing.
Strikers Andy Carroll and Luis Suarez were signed in January.
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