The hotly anticipated production, which opened to mixed reviews last year, is up for seven awards including best new musical and best actress in a musical for Sierra Boggess.
This year’s awards, the highest honour for London theatre, are being relaunched to take on the Tonys, the headline-grabbing US ceremony.
After The Dance, by Terence Rattigan at the National Theatre, is up for six nods, including best actress (Nancy Carroll), director and revival.
King Lear, at the Donmar Warehouse, has five nominations, including best actor for Sir Derek Jacobi, director (Michael Grandage), supporting actress (Gina McKee) and revival.
Tamsin Greig and David Suchet have also been nominated for best acting awards.
Suchet is up for his role in All My Sons at the Apollo Theatre, while Episodes actress Greig is nominated for The Little Dog Laughed at the Garrick.
Organisers hailed an unprecedented standard in the best actor category – which also sees Rory Kinnear in the shortlist for Hamlet, Roger Allam for Henry IV at Shakespeare’s Globe and Mark Rylance for La Bete at the Comedy Theatre.
Legally Blonde is pitted against Love Never Dies for best new musical, with its star Sheridan Smith up for best actress in a musical.
Organisers want to “revitalise” the Olivier Awards, established in 1976 as the Society of West End Theatre Awards.
There will be live red carpet coverage on BBC News while the full ceremony will be broadcast on Radio 2 and on TV via the red button.
The event, sponsored by MasterCard, takes place on Sunday March 13 at the Theatre Royal Drury Lane.
The president of the Society of London Theatre which organises the awards, Nica Burns, said London theatre was a “ray of sunshine in a grim world”.
She said: “It’s something we should be out celebrating. We have now had seven years of continuous growth and why? It’s because we’re incredibly good at it.”
Whittling down the shortlist took “a marathon six hours which was ...really, really hotly debated,” she added.
She added: “The Tonys have put on some great shows, with the likes of Elton John and Liza Minnelli on stage. We do feel that we can improve the awards.”