Negredo's previous deal expired in 2014 and he has become a key contributor at the Ramon Sanchez Pizjuan ever since he joined Sevilla from Real Madrid in the summer of 2009.
The 26-year-old netted 37 times in all competitions in his first two seasons at the club attracting the interest of some of Europe's big teams along the way. Sevilla have been able to set Negredo's buy-out clause to €50 million with the new deal.
"I told president Jose Maria del Nido I did not want to leave, that I really liked being at Sevilla," Negredo told A Balon Parado.
"I am lucky and happy to be at the club, who took me in and gave me this opportunity.
"I have never made a decision which was better than this one. I did not need to be convinced. I am very happy and satisfied."
Spanish media report that Real Madrid decided against exercising their buy-back option for the striker.
Sevilla paid Madrid €15million for the striker two years ago.