“For me, I have made the best decision in my career.”
The Senegal international scored 10 goals as Liverpool reached last season’s Champions League final, and has started the new campaign strongly, netting six times in 11 Premier League games.
He was also named on the 30-man shortlist for the Ballon d’Or last month.
The length of his new deal was not disclosed by Liverpool.
“This is a big boost for everyone and another demonstration of how the players we have at this club are committed, not just to our present but our future also,” said Reds manager Klopp.
“I can’t think of a single club anywhere in Europe that wouldn’t want a player like Sadio available to them, so the fact he wants to remain with us says something about where we are currently.
“He is a such an important member of our team and squad. He radiates joy and I think this is reflected in his performances and impact on the pitch.”
The Anfield club put their unbeaten record in the league this term on the line against Watford on Saturday.