Thompson, 34, left Golden State this week in free agency after spending the entirety of his 13-season NBA career with the team.
A key part of Golden State's championship-winning seasons in 2015, 2017, 2018 and 2022, Thompson is reportedly set to join the Dallas Mavericks next season.
Thompson, widely regarded as one of the greatest shooters in basketball history, said in a message on Instagram that he had been "honored" to play for the franchise.
"There are not enough words and images to convey how I really feel about y'all," Thompson wrote. "From the bottom of my heart, thank you so much for the best times of my life.
"I really just wanted to be the best I could be and help bring as many championships as possible to the region.
"The best part was not the rings though, it was the friendships I made that will last a lifetime.
"My family and I would like to thank all of the amazing people who work tirelessly to make the @warriors organization world-class.
"Don't be sad it's over, be happy it happened. Until we meet again. Sea captain out," Thompson concluded, signing off with the affectionate nickname acquired due to his habit of commuting to Warriors home games at their waterfront arena on his personal pleasure boat.
