The show, which is a revival of the 1993 West End production, will open at the Piccadilly Theatre on Aug. 8 following previews that begin July 25.
The television judging panel included producer David Ian, promoter David Gest (best known as Liza Minnelli's ex) and choreographer Brain Friedman, who has choreographed for Britney Spears.
Their objective was to find the next Sandy and Danny, the roles made famous by Olivia Newton-John and John Travolta in the 1978 movie version of the Jim Jacobs and Warren Casey musical. Those roles were created on the Broadway stage by Carole Demas and Barry Bostwick.
The movie was screened by ITV prior to the final episode of "Grease is the Word."
McFadden, 24, is the sister of pop star Brian McFadden. "The first thing I'm going to do is drink a big bottle of champagne. I worked very hard to get here," said McFadden. Bayne, 19, said, "It's an amazing feeling to be here and I never thought I'd get here. I'm just a college boy, but I'm really thankful."
Grease received its world premiere as a play with music in Chicago's Kingston Mines Theatre in 1971, before reaching Broadway's Broadhurst Theatre as a fully staged musical the following year.
For more on Grease, call (0)844 412 6666.