Minor replaces longtime music director Kevin Eubanks, who on Monday's show made his May 28 exit date official.
In an announcement Tuesday, NBC said Minor is expected to debut at "Tonight" on June 7.
The current season of "American Idol" ends in late May, after which Minor will continue to consult with "Idol" creator Simon Fuller on various projects, NBC said.
Minor has also served as music director of the Super Bowl, the Grammy Awards and "The NAACP Image Awards."
His 2009 book, "There's No Traffic on the Extra Mile," shares his recollections of collaborating with such performing artists as Whitney Houston, Christina Aguilera, Alicia Keys, Ray Charles and Beyonce.
"We couldn't be more excited," said Debbie Vickers, "Tonight" executive producer. She said the show "has a long tradition of acclaimed musicians in this role, and it's great to now include Rickey alongside Kevin and Branford (Marsalis)."
Eubanks has been aboard "Tonight" since Leno took over as host in 1992. He became music director when Marsalis left in 1995, with duties that included strumming the guitar and playing Leno's comic sidekick. In February, NBC said Eubanks had expressed interest in personal touring and recording.