The Spaniard signed for the Reds from St James' Park in 2011 and has since racked up 75 appearances for the Merseyside outfit.
"It was one of the best decisions in my life, in terms of football," Enrique told the club's official website.
"Of course, I already played for a good club at Newcastle, but you can't compare one club with the other in terms of history.
"I'm really happy with my decision to be here. It's my second season and I'm playing a lot, like last year. I'm improving a lot as a player and a person as well."
Enrique was part of the team who defeated his former club 6-0 on Tyneside.