Harry Potter and the Cursed Child is expected to follow both these West End hits by opening on Broadway next year.
Kenneth Branagh will be honored for his contribution to theatre during Sunday's black-tie ceremony at London's Royal Albert Hall.
"Harry Potter and the Cursed Child" emerged as a big victor at the 2017 Olivier Awards, with wins in nine categories.
The two-part play co-written by JK Rowling, which launched at London's Palace Theatre last July, was named Best New Play at the UK's top theatre awards last night (April 9).
Best Actor in a Supporting Role (Anthony Boyle), Best Actress in a Supporting Role (Noma Dumezweni) and Best Director (John Tiffany).
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But star Jamie Parker, who won the best-actor prize for playing the adult Harry, said success - and the embrace of Potter fans - had not been a foregone conclusion.
Noma Dumezweni, who plays Hermione Grainger, won best supporting actress. I've seen the evidence.
"It's all about enjoying the role, which is a amusing thing to say when you are playing somebody who would arguably have post-traumatic stress syndrome".
Hilariously repetitive comedy "Groundhog Day" was named best new musical.
Other winners included Billie Piper for Best Actress for her role in "Yerma", which also won Best Revival.
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Conductor Mark Wigglesworth won the outstanding achievement in opera award for his conducting of "Lulu" and of "Don Giovanni" at the Royal Opera House, and "Akhnaten" was named best new opera production.
Two shows composed by Andrew Lloyd Webber also scooped awards.
The Olivier Awards have become an increasingly glitzy affair in recent years, awarded at a ceremony studded with musical numbers, modeled on Broadway's Tony's.
Named in honor of British acting legend Laurence Olivier, the Olivier Awards recognize excellence in professional theater in London.
Celebrities walking the carpet and handing out trophies included "Star Wars" actor John Boyega, Oscar victor Mark Rylance, "The Good Wife" star Cush Jumbo and "Hamilton" creator Lin-Manuel Miranda.
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"Our fearless men and women in uniform make tremendous sacrifices", said the candidate, who believes a stint in the U.S. Ted Cruz plans to campaign with Estes in Wichita on Monday, and Vice President Mike Pence and U.S.