Costello and his band, the Sugarcanes, perform at the New York Public Library in Manhattan.
The music series is known for hosting artists in shows at unusual, intimate settings.
Other artists lined up for the third season include Robert Plant, Ray LaMontagne, Grace Potter and the Nocturnals, Daniel Merriweather, A Fine Frenzy and Lisa Hannigan.
Plant plays at the War Memorial Auditorium in Nashville, Tenn.
Says the former Led Zeppelin singer: "To work your craft, you've got to be close with your musicians. So I enjoy intimacy now. I can't say that I'd be in a hurry to go back to Madison Square Garden again."