Based on the popular British movie, the show about a coal miner's son who dreams of becoming a dancer, will compete for best musical against "Next to Normal," "Rock of Ages" and "Shrek The Musical."
"It's been an amazing experience," Elton John, nominated for the show's original score, told CBS' "Early Show," which telecast early nominations. "It's made an incredible impact on my life."
Best-play nominations went to "God of Carnage," "Dividing the Estate," "reasons to be pretty" and "33 Variations."
"Next to Normal," a heartfelt musical about a woman battling mental illness, received 11 nominations, while "Shrek" and the revival of "Hair" tied with eight each.
In several of the acting categories, performers from the same show will competing against each other.
For best-actor play, James Gandolfini and Jeff Daniels, stars of "God of Carnage," will go up against each other. So will their two co-stars in Yasmina Reza's scathing comedy of manners - Marcia Gay Harden and Hope Davis - in the actress-play category.
Other actor-play nominees were Raul Esparza, "Speed-the-Plow"; Geoffrey Rush, "Exit the King"; and Thomas Sadoski, "reasons to be pretty."
The two royal ladies of "Mary Stuart" - Janet McTeer as Mary, Queen of Scots, and Harriet Walter as Elizabeth I - will also battle for the actress nod. The last slot in the category was filled by Jane Fonda, who portrays a dying musicologist in "33 Variations."
In one of the more unusual nominations, the three boys who share the title role in "Billy Elliot" - David Alvarez, Trent Kowalik, Kiril Kulish - were nominated together for the best actor-musical prize.
Their competition: Gavin Creel, "Hair"; Brian d'Arcy James, "Shrek The Musical"; Constantine Maroulis, "Rock of Ages"; and J. Robert Spencer, "Next to Normal."
Joesefina Scaglione, Maria in the revival of "West Side Story," picked up an actress-musical nomination. She will compete against Stockard Channing, "Pal Joey"; Sutton Foster, "Shrek"; Allison Janney, "9 to 5: The Musical"; and Alice Ripley, "Next to Normal."
Winners will be announced June 7 at Radio City Music Hall.