He replaces Kevin Eubanks, who made his May 28 departure date official on Monday.
In an announcement Tuesday, NBC says Minor is expected to debut on the show June 7.
Minor is the music director of "American Idol," whose season ends in late May. He will continue to consult with "American Idol" creator Simon Fuller on various projects.
Minor has also served as music director of the Super Bowl, the Grammy Awards and "The NAACP Image Awards."
Eubanks has been aboard "Tonight" since Leno took over as host in 1992. He became music director when Branford Marsalis left in 1995.
