The Salt Lake Tribune first reported the Jazz's interest in Jones and his candidacy for an assistant job.
Jones returns to the Jazz after spending the previous two seasons as head coach of the San Antonio-owned Austin Toros of the Development League.
Before joining Austin, Jones spent three seasons as the original head coach of the D-League's Utah Flash.
"We have a relationship," Jazz coach Tyrone Corbin said. "He's been around the organization for those years and … he understood how we did things around the organization, and he went to a great organization in San Antonio. I thought he did a great job there."
Corbin said Sanders deserved a promotion after spending the 2011-12 season primarily training young Jazz big men Enes Kanter and Derrick Favors. Despite Sanders taking a full-time assistant role, Utah doesn't plan to hire a specific big-man coach.
"We're going to do it by committee. If there's an opportunity to add a piece or two here down the road, we'll explore that," Corbin said. "But the way things are right now, I'm happy with the guys I have on staff."
Corbin's four-person staff is rounded out by Sidney Lowe and Jeff Hornacek. Jones replaces former assistant Scott Layden, who was named Wednesday as the Spurs' assistant general manager.
Utah's coaches will convene during the third week of the month as they prepare for training camp, which is expected to begin Oct. 2.
"I'm anxious to get started, because we have so much expectation of where and who we are and how to get better," Corbin said.
He added: "There's a lot of questions still around. We have to build a team again. That's going to be working every day from day one, to understanding who we are and how we have to work together to be an effective team on the floor."