He sent the letter to the San Antonio Express-News.
The two-time All-Star was shipped to Toronto on July 18 -- along with Danny Green and cash -- in exchange for DeMar DeRozan, Jacob Poeltl and a 2019 first-round pick in the NBA Draft.
"I have been going back and forth the last few weeks trying to figure out the right things to say, and it comes down to two simple words: Thank you," Leonard wrote in his statement.
"My family and I want to say thank you to the entire Spurs organization and the people and fans of San Antonio."
Leonard also thanked each of his teammates during his seven year stay with the franchise. He then thanked Spurs coach Gregg Popovich and the fans.
"Through all the ups and downs -- I'm glad there were many more ups! -- I'll never forget what we have shared and accomplished together," Leonard wrote.
"While I'm looking forward to the next chapter in my career, I'll always remember the city and the people of San Antonio."
Leonard averaged 16.2 points, 4.7 rebounds, 2.3 assists, 2.0 steals and one block per game in nine games last season for the Spurs. He posted a career-best 25.5 points per game during the 2016-17 season. That year, Leonard also averaged 5.8 rebounds and a career-best 3.5 assists per bout.