The Nigeria international, who joined from Manchester City in August 2017, has agreed to a deal that will run until at least the end of the 2023-2024 season.
"I can't express how I'm feeling," Iheanacho, who has scored 12 goals this season, said. "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."
Iheanacho has hit a rich vein of form after previously struggling for Leicester, the 24-year-old having scored seven goals in his previous four appearances.
His five top-flight goals in March, including a hat-trick against Sheffield United, helped him to win the Premier League Player of the Month award, while he also struck the opener in Leicester's 3-1 FA Cup quarter-final win over Manchester United.
His minutes-per-goal rate last month (48) was bettered only by Bayern Munich star Robert Lewandowski (38.75) across Europe's top-five leagues.
In total, he has scored 32 goals in 117 games for Leicester, leaving manager Brendan Rodgers delighted with his recent performances and his overall attitude.
"Since he has come into the team he has just been fantastic," Rodgers said. "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."