Ujiri made the announcement to reporters during his season-ending media availability Tuesday.
"I love it here. My family loves it here. My wife loves it here, which is very important. My kids are Canadians. You want to win more. ... In my mind, I'm here," Ujiri said.
Earlier this month, league sources told ESPN that the Washington Wizards were preparing to offer Ujiri a deal approaching $10 million annually with an opportunity for ownership equity.
Ujiri, who has two years left on his contract, is the architect of the first championship in Raptors history. He also helped to build the Denver Nuggets into a contender.
The 48-year-old Ujiri now will focus on retaining NBA Finals MVP Kawhi Leonard, who is expected to opt out of the final year of his contract and become a free agent.
Ujiri said he texted with Leonard as recently as Monday night and talked to Leonard's uncle and adviser, Dennis Robertson, earlier on Tuesday. Ujiri said he's "confident" Leonard will decide to return to Toronto.
"We'll wait. He's our player and he's a superstar on our team and we'll wait on that," Ujiri said.
Ujiri stressed the main selling points of his pitch to Leonard: health, trust, success.
"I said we have to be ourselves, and we were ourselves for the whole year,'' Ujiri said. "I think he saw that. I think we built a trust there.
"I believe winning a championship, him seeing who we are, working with his medical staff combined with our medical staff and getting him to where he wanted to be,'' Ujiri added.
"I think they know what the effect of Kawhi's decision is, but we're really approaching it like we want to bring everybody back on this team,'' Ujiri said. "That's a priority for us.''
Center Marc Gasol also has a player option for next season, and Green is a free agent.
Less urgent is a potential extension for forward Pascal Siakam, a runaway winner of the NBA's Most Improved Player award. The parties plan to meet during the summer league.
"Pascal has gotten to a place where he's definitely a priority for us and it's definitely going to be a conversation that we'll have,'' Ujiri said.
Ujiri said little about his confrontation with a deputy following the Game 6 clincher. The deputy's lawyer, David Mastagni, says his client is on medical leave with a concussion and jaw injury and is considering a lawsuit. Ujiri says his lawyers are updating him about the investigation.
"I am confident about who I am as a person, my character and as a human being,'' Ujiri said. "For now, I'll just respect their process there and wait for the next steps.''
Ujiri finished fourth in voting for the NBA Executive of the Year award, won by Milwaukee Bucks general manager Jon Horst.
The Associated Press contributed to this report.