Iheanacho joined the Foxes from Leicester City in the summer of 2017 and has so far made 117 appearances at the King Power Stadium, scoring 32 goals.
The 24-year-old Nigerian international has hit a rich vein of form in recent months, scoring four goals in his last seven appearances for Leicester City.
His impressive performances for Brendan Rodgers’ men saw him named as the Premier League’s player of the month for March.
"I can't express how I'm feeling," Iheanacho, who has scored 12 goals this season, told the club's website. "I'm excited, I'm happy, I'm overwhelmed! It's a great moment and I'm happy that Leicester City gave me a new contract.
"It's been a great time here. It's not been easy, but there's a lot of people here that are good people, great people to work with. They are nice people and they make me feel comfortable and welcome since I came in.
"It's been really great being here. It's like a family. I'm happy being here and hopefully I can stay here many more years."
"Since he has come into the team he has just been fantastic," Leicester manager Rodgers told Sky Sports.
"I am delighted for him because he is such a conscientious guy, such an honest guy, and as you can see now, a very talented player.
"All the guys love him. Now what you are starting to see is all his qualities. How he receives the ball. His strength. His finishing ability. His anticipation as a striker. You are seeing all of these things now because he is playing with confidence. I am delighted for him."
