Suarez says he was a big fan of the 32 year-old growing up.
"It's hard to find words to describe what a great player Steven has been - and continues to be - for the club," Suarez told liverpoolfc.com.
"It was only four years ago or so that I was playing on the Playstation and I was always Liverpool and to have him in my team was great. Now I'm playing alongside him - he was a hero.
"I'm very, very happy here at the club, I couldn't be happier. Liverpool is a club I've always dreamt of playing at. It's like a dream for me."