There have been reports that the point guard could be interested in leaving the team following a series of summer departures.
The 27-year-old told Comcast SportsNet: "I love it here. The fans are great here. And [president of basketball operations] Danny [Ainge] has been straightforward with me. This is my team. Why would I want to leave? Why would I want out?
"I never really backed away from a challenge. This would be a challenge. I'm looking forward to working with coach [Brad] Stevens.
"It's a brand-new start for us as a team. A lot of new players and a lot of young guys willing to listen, so I'm very excited about that."
Rondo averaged a career-high 13.7 points per game last year.