The 29-year-old Portugal international, who joined the club on an initial loan deal from English side Reading in 2013, has gone on to make 112 appearances and scored six goals for the club.
Carrico has gone on to help Sevilla win three Europa League titles and reach the final of the Copa del Rey during his stint at the Estadio Ramón Sanchez Pizjuan.
His new deal means he is now the joint-longest serving player in the Sevilla squad alongside Nico Pareja.
Foxes' January recruit Kamal Sowah says although Bayern Munich and Man City were interested, Leicester wanted him the most.
Reports claim that Arsenal are set to move for on-loan Lyon midfielder Tanguy Ndombele at the end of the season.
Ben Chilwell insists the Leicester City squad are focused on finishing the season well in order to qualify for the Europa League.