The Uruguayan has committed to the club for a further four-and-a-half years.
He will earn £160,000 until the end of this season and then £200,000 per week over the next four years.
"I am delighted to have agreed a new deal with Liverpool and have my future secured for the long term," he said.
"I believe I can achieve the ambitions of winning trophies and playing at the very highest level with Liverpool. My aim is to help get us there as quickly as possible."