Richards is best known for his starring role in Saturday Night Fever at the London Palladium and for his role as Jerry Lukowski in The Full Monty at The Prince of Wales Theatre.
He will join Caroline Sheen (Les Misérables, Mamma Mia!, The Witches Of Eastwick) as Sandy and Lee Latchford Evans, from Steps, as Teen Angel.
Grease may still be best remembered as the 1970's movie starring John Travolta and Olivia Newton John, but it was a stage musical before that (in which a young Richard Gere appeared in the West End) and has been a hugely popular night out ever since.