Vaughn, 37, replaces Stan Van Gundy, who was fired after the season.
Vaughn spent the last two seasons as an assistant coach for the San Antonio Spurs. He helped them win the NBA championship in 2007 before retiring as a player.
The Magic had been looking for a new coach since letting go of Van Gundy and general manager Otis Smith on May 21. Rob Hennigan was hired as the GM on June 20.
"We are beyond excited to name Jacque Vaughn as our head coach," Hennigan said in a statement. "As we navigated through our coaching search, we quickly saw that Jacque's spirit and leadership strengths made him the clear choice."
Vaughn will be introduced at a news conference on Monday.
Vaughn is the 10th coach in the team's history. He also worked with Hennigan with the Spurs while Hennigan was in the team's basketball operations department.
"We are confident that his diligence, attention to detail and communication style will help establish the bedrock of our culture moving forward," Hennigan said in the statement. "His commitment and passion to building a sustainable program will help steer our organization for years to come."
As a player, Vaughn played 12 seasons in the NBA, including his last three with San Antonio. He averaged 4.5 points and 2.5 assists in 776 career games.
He starred collegiately at Kansas, where he is second on the all-time assists list with 804.
Utah Jazz assistant Jeff Hornacek, Phoenix Suns player development coach Lindsey Hunter, Golden State Warriors assistant Michael Malone and Indiana Pacers assistant Brian Shaw were also candidates for the Magic job, according to the Orlando Sentinel.
--The Memphis Grizzlies re-signed center Hamed Haddadi, the team announced Saturday.
Terms of the deal were not disclosed.
The first Iranian ever to play in the NBA, Haddadi averaged 2.0 points, 2.0 rebounds and a career-high 0.74 blocks in 5.9 minutes in 35 games for Memphis last season. He also shot 54.2 percent from the field. He has played all four seasons of his NBA career with Memphis.