Terms were not disclosed by the Jazz on Wednesday but sources told ESPN's Adrian Wojnarowski that Hardy received a five-year deal.
Hardy, 34, will be the youngest active head coach in the NBA.
Hardy was one of four finalists who met with ownership in Salt Lake this week, including Celtics assistant Joe Mazzulla, Raptors assistant Adrian Griffin and Jazz assistant Alex Jensen, sources said.
The Jazz, led by new CEO Danny Ainge, conducted an extensive search that included at least 15 candidates to replace Quin Snyder, who resigned earlier this month. After taking over a rebuilding team, Snyder had a 372-264 record during his eight-season tenure in Utah, which has an active six-year postseason streak but did not advance past the Western Conference semifinals in that span.
Hardy spent one season with the Celtics as an assistant coach under Ime Udoka, helping Boston advance to the NBA Finals.
Hardy, who played at Division III Williams College, began his career as a video coordinator for the San Antonio Spurs before being promoted to an assistant coach under Gregg Popovich. He also served as the head coach of San Antonio's summer league team for four years.
The Jazz are also making a front-office hire, as David Fizdale has agreed to become an associate general manager, sources told Wojnarowski.
After 18 seasons as an NBA head coach and assistant coach, Fizdale will move into management and work closely with Ainge and GM Justin Zanik.