Costello will preside over the show and John will be one of its executive producers.
The series is to air this year on CTV in Canada, Channel 4 in the United Kingdom and the Sundance Channel in the United States.
The Sundance Channel said the series will include 13 one-hour programs that will serve as a forum for in-depth discussion and performance with artists and personalities.
"I'm not interested in extracting some dark secret. I'd rather hear about a bright secret, a deep love or a curiosity that might be otherwise obscured by fame," Costello said in a statement. "This is a wonderful opportunity to talk in complete thoughts about music, movies, art or even vaudeville, then frame it with unique and illustrative performances."
"Elvis Costello is the foremost expert on popular music," said John. "I thought it would be sensational to use his knowledge and intelligence to explore the artistry of musicians and other fascinating people involved in making great music, as well as true music aficionados."