Gobert has played professionally in France for three years. Last season for Cholet, he averaged 13.4 points, 5.4 rebounds and 1.9 blocked shots.
In return for Gobert, the Jazz sent the Nuggets the 46th pick in the draft and an undisclosed amount of cash. The Nuggets used the pick on Virginia Tech point guard Erik Green.
"I feel great," Gobert told reporters in Brooklyn. "It was my dream since I'm a kid. I feel great."
Asked what he can bring to Utah, he said, "It will be great. I can bring defense, block shots, rebound, and bring my offensive game to help the team to win. Getting better month by month."
Gobert's length and 7-foot-9 wingspan make him an intriguing NBA prospect. He runs well for his size and has good mobility around the basket.
Offensively, Gobert needs to polish his game. But with Derrick Favors and Enes Kanter established as the leaders of the Jazz's big-man rotation, the Jazz can take their time in developing Gobert.
"I'm getting better on my shot and my post game," he said. "... [But] I have to get stronger in my legs and upper body and get weight [so] I can be the best I can be."
Three weeks ago, Gobert came to Utah for a pre-draft workout.
At that time, he said, "I'm a defensive player, I block shots, get rebounds, work in the paint and bring energy. That's what I think I can bring in my first year."
According to Gobert, he enjoys helping his teammates, saying he likes to "help defensively and offensively, to put them in a good position [with] good passes and good screens for open shots."