The 36-year-old, who recently signed a new one-year deal with the club, will complete his 14th season with the Tigers next year.
"I'm really excited about next year. I'd got it in my head that I was leaving and to then find out that I was actually staying was a relief in some ways and it was quite a strange situation," he told BBC Sport.
"I'm very pleased to be staying. I do hold a special place in my heart for the club."
Chuter made 24 appearances for his country.