John's musical beat the favorite, "Mary Poppins," during the ceremony at London's Savoy Hotel. The Broadway-bound "Mary Poppins" took the prize in the design category, the BBC reported.
In accepting his award, John said creating "Billy Elliot" was one of his "most enjoyable" experiences. "The more I work in theater the more I love it," he added.
"The Philanthropist" star Simon Russell Beale chalked up his third best actor award and Harriet Stuart was named best actress for her role in "Mary Stewart," the BBC reported.
Michael Grandage was named best director in both the drama and musical categories for "Don Carlos" and "Grand Hotel."
The Royal Court Theater, which celebrates its 50th birthday in April, received a special award for its contribution to the British stage.
Celebrity Families of 2014 [PHOTOS]