Dunne joined the cast and creative team of Riverdance in October 1995. He was initially invited to choreograph and perform the newly commissioned number "Trading Taps" with Tarik Winston. However, with the departure of original male lead and choreographer Michael Flatley the day before the re-opening of the show at The Apollo in London, he found himself taking over the principal role at short notice. He toured with the production for three years, taking the show to its USA premieres in New York (Radio City Music Hall) and Los Angeles (Pantages Theatre), and also to Australia. His performances were recorded for the "Riverdance: Live From New York City (1996)" DVD. Further choreography credits for the production followed; Firedance (with María Pagés), Heartbeat of the World (with María Pagés) and Heartland Duet (with Jean Butler). Special TV appearances during these years include The Royal Variety Show (The Dominion London), The Kennedy Honours (Kennedy Centre Washington D.C.), and The Grammy Awards (including a duet with Savion Glover) at Madison Square Garden, New York.