Sweeney, 41, will not begin his new duties until the Spurs have finished the best-of-seven NBA Finals, which begin against the New York Knicks in Texas on Wednesday.
Sweeney has served as an NBA assistant coach since 2013 with Brooklyn, following two years as a video coordinator for the Nets. He later served on staffs at Milwaukee, Detroit, and Dallas before joining the Spurs last June.
"Sean brings a tremendous work ethic and a high degree of intensity that set the tone for everything he does," Magic president of basketball operations Jeff Weltman said.
"Sean's attention to detail and his ability to communicate and teach the game clearly stand out. He’s grounded in competitiveness and accountability while also embracing a modern, creative approach to coaching."
The Magic fired head coach Jamahl Mosley last month after Orlando blew a 3-1 series lead and lost to Detroit in the first round of the NBA playoffs. Mosley was hired as head coach in New Orleans two weeks later.
Orlando has not won an NBA playoff series since reaching the Eastern Conference finals in 2010, losing seven times in the first round and missing the playoffs in nine campaigns.