In exchange, the Warriors will receive veteran forward Gerald Wallace, according to multiple reports.
"Want to take a moment to thank the entire Bay Area for what's been the best 5 years of my life," Lee wrote Monday on Instagram. "The journey from a 23 win team to NBA champs is one I'll never forget. Thanks to the most loyal fans in basketball for supporting me the entire way!
"This season's success happened because of the amazing character and chemistry from the 15 men on the roster, the front office, coaches, and staff all wanting the same thing, to win a championship."
Lee, a two-time NBA All-Star (2010, 2013), appeared in 49 regular-season games, making four starts, because of injury and the emergence of Draymond Green, who recently agreed to return to the Warriors on a five-year contract worth $85 million.
"For him to come in after the way this season has gone, the fact that his dumb coach hasn't played him enough probably, he's kept his attitude up," Warriors Coach Steve Kerr told the San Jose Mercury News during the NBA Finals against the Cleveland Cavaliers.
Lee, who was the team's highest-paid player last season, averaged 7.9 points with 5.2 rebounds in just over 18 minutes per game this season -- all near career-lows.
"I have had to make some adjustments to kind of learn the role, because it's just not anything I've done at any point in my basketball career," Lee said at the time. "I hope that I'm better at playing that role now than I was a couple of months ago, and hopefully I'll continue to be good at it moving forward."
Lee will earn $15.4 million next season with the Celtics in the final year of a six-year, $80-million deal he originally signed with the Warriors in 2010.
Lee, 32, averaged 16.7 points with 9.3 rebounds per game over five seasons with the Warriors. He was drafted out of Florida by the New York Knicks with the 30th overall pick in 2005.
Wallace, 32, has been on five teams in 14 seasons. He's spent the last two years with Boston, appearing in 90 games, averaging 3.7 points with three rebounds per game.
Follow Matt Wilhalme on Twitter @mattwilhalme