W won the brief after a "competitive audition" and will work on all PR for all phases of the project, including construction, the opening in late 2020, and beyond.
LW Theatres owns and operates some of the most prestigious theatres in the world, including the London Palladium and Theatre Royal Drury Lane.
The business is wholly owned by Andrew Lloyd Webber and hosts some of the top musicals and plays, as well as a variety of concerts and comedy.
Built in 1663, Theatre Royal Drury Lane is the oldest theatre site in the world in continuous use, and renowned for its Victorian melodramas and pantomimes.
Since 1920, its history has mirrored the development of the modern musical, hosting premieres of Show Boat, Oklahoma!, Carousel, South Pacific, My Fair Lady and Miss Saigon.
W said it will "draw from its considerable place-making expertise and cultural connectivity" to make Theatre Royal Drury Lane "one of the most anticipated openings of 2020".
LW Theatres chief executive Rebecca Kane Burton said: "LW Theatres has a bold vision for Theatre Royal Drury Lane, and that means we were looking for an agile, smart agency, with strong ideas and great industry knowledge to help us reopen the venue as the hottest destination of 2020.
"W impressed with the right mix of consumer and destination expertise, with the perfect team to support us across all disciplines as we roll out that ambition. I'm looking forward to working with them."
W founder Warren Johnson added: "For an agency that prides itself on being at the heart of London culture, this was the brief of the year to win. We look forward to working alongside LW Theatres on communicating its exciting vision for Theatre Royal Drury Lane."
W Communications was recently shortlisted as one of PRWeek's Agencies of the Decade. In September, the agency set sail with Royal Caribbean International.