It also won for choreography, sound and outstanding achievement in music. Kobna Holdbrook-Smith won best actor in a musical for playing charismatic, abusive Ike Turner in "Tina - The Tina Turner Musical."
Best actress in a musical went to Sharon D. Clarke for her powerful performance in Tony Kushner's "Caroline, or Change." as the maid to a family in the American south in the 1960s.
"The Inheritance" has been named best new play at British theater's Olivier Awards.
Matthew Lopez's epic drama took the first trophy at a Sunday evening ceremony for the annual prizes, Britain's equivalent of the Tonys.
The American playwright said he was "overwhelmed and overjoyed" to win the London stage award for his seven-hour play about young gay men in New York.
Laura Wade's "Home I'm Darling," about a 21st-century couple trying to live a perfect 1950s life, was named best new comedy.
"The Inheritance" has eight Olivier nominations in all. Musicals "Come From Away" and "Company" are each nominated in nine categories.
The prizes are being handed out in a black-tie ceremony at London's Royal Albert Hall.
Actors and other theater professionals are preparing for Britain's annual Olivier Awards ceremony, where musicals "Come From Away" and "Company" lead the nominations with nine apiece.
"Come From Away," about a Newfoundland town that sheltered stranded air travelers after the 9/11 attacks, is up for best new musical. A gender-switched West End production of Stephen Sondheim's "Company" is nominated for best musical revival.
Epic gay-history drama "The Inheritance" has eight nominations, and a revival of Rodgers and Hammerstein's "The King and I" starring Kelli O'Hara and Ken Watanabe has six.
Acting contenders include Ian McKellen for "King Lear," Gillian Anderson for "All About Eve" and Sophie Okonedo for "Antony and Cleopatra."
Sally Field, Kelsey Grammer, Tom Hiddleston and Wendell Pierce are among the stars expected at Sunday's ceremony at London's Royal Albert Hall.