The Boys, Neil Tennant and Chris Lowe, have a nine-day residency in June. It will be the first time a pop band has performed at the theatre, which was built by Richard D'Oyly Carte for the Gilbert and Sullivan shows.
His company enjoyed huge success there with performances of Gilbert and Sullivan's best-known works, including The Mikado and The Gondoliers.
To a Pet Shop Boys fan the operas may seem distinctly untrendy, but in their time they were the Spitting Image of their day, loved by audiences for their sharp satirical wit.
According to the impresario Harvey Goldsmith, the Pet Shop Boys requested a West End venue for their new show Somewhere, named after their latest single - a cover of the song from West Side Story. The production involves live music, video footage and closed-circuit television.
"The Savoy has the right look, feel and size for the intimacy of the new piece. The Pet Shop Boys have always been interested in the theatrical side of music and they've always done something different," Mr Goldsmith said.
Stephen Waley-Cohen, the venue's managing director, said the event might well come as a surprise to the patrons of the theatre and its next-door neighbour, the Savoy hotel.
"The customers of the Savoy, our owner and neighbour, may well not attend the shows after a quick gin and tonic in the hotel in the numbers they normally do," he said.
"But the Pet Shop Boy's sophisticated and intelligent fans will more than fit in with the history of the Savoy Theatre."