The 57-year-old soap star, who plays Nick Cotton in the BBC soap, has played the role previously on regional tours.
"It's always been my ambition to play Billy in the West End," he told The Sun.
Jerry Springer is currently starring in the classic stage musical in London. Previous EastEnders actors to appear in the show include Michael Greco (Beppe di Marco), Jill Halfpenny (Kate Mitchell) and Emma Barton (Honey Mitchell).
Altman's soap character has recently been involved in an explosive storyline with Dot (June Brown) and Dotty (Molly Conlin).
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