"I've just started a phase of my career which I always dreamed about and wanted to do, which is to play for Liverpool," said the Uruguayan forward.
"I have five years left on my contract and I think beyond that, I'm already thinking about staying many more years at Liverpool.
"It's a club I like. I feel very good about being here, about being in the city.
"I feel very pleased. It would be difficult to match the atmosphere, hunger for success and glory that this club has at another team."