The Holland international, who joined the Reds from Feyenoord in 2006, was contracted until next summer but has been rewarded for his form this season.
In a news release issued by Sport-Promotion, the 30-year-old said: "I am very happy. We have spent a long time (in discussions) but always with the intention to reach an agreement.
"All the conversations were conducted in a friendly atmosphere.
"It fits perfectly with the feeling I got at this club.
"Since the day I first walked in, I felt welcome. That feeling has never left."
The release added that Kuyt had been discussing new terms with the club for the past month.