Neil Tennant and Chris Lowe will play the Playhouse on 22 February.
Pet Shop Boys last played the Capital when they headlined the Concert in the Gardens at Edinburgh’s Hogmanay 2013/14.
Earlier this year, Chris revealed during a BBC Radio 2 documentary that they were also thinking of bringing a show to the Fringe in the future.
He said, “We have been in discussion with Jonathan Harvey about writing a one woman show for Billie Trix, played by Frances Barber, and taking it to Edinburgh - Edinburgh doesn’t know about this by the way.”
In the new show, which Neil described as “almost like a cabaret piece” the character, an ageing club hostess, would “tell us the story of her life and sing us a few songs,” Chris continued, adding, “We are very excited about that and hopefully that will happen.”