Welts has been with the franchise since 2011. He has also worked with the Seattle SuperSonics, Phoenix Suns, and the league office in multiple roles over 46 years.
He'll stay with Golden State as an advisor after stepping down.
"This has been the ride of a lifetime," Welts said in a statement. "To have had a front row seat to the growth of the NBA from where it was in the late 1960s to its place today as one of the most respected and successful leagues in sports on a global stage has been an incredible privilege.
"The first day I met (Warriors co-owners) Joe Lacob and Peter Guber, I wanted to be a part of building what I knew could be a special organization. We have the most talented staff in the industry, and we are poised for even greater success in the future. Personally, I am excited for my own next chapter."
Welts was inducted into the Hall of Fame in 2018. In 2011, the 68-year-old became the highest-ranking sports executive to publicly acknowledge he's gay.
During his decade in Golden State, Welts has overseen and helped craft one of the NBA's greatest dynasties. The team made five consecutive NBA Finals between 2015 and 2019, winning three championships and completing a record-breaking 73-win season in 2015-16.
He also oversaw the club's move from Oakland back to San Francisco ahead of the 2019-20 campaign.
The Warriors expect to name a new president within the next week.