The Traverse Theatre began life in 1963 as a theatre club in an abandoned brothel in Edinburgh's Lawnmarket. The theatre is so named because its first Artistic Director, Terry Lane, mistakenly believed that the staging arrangement is called 'traverse'. He later realised that it is 'transverse' but it was already too well known to change it.

In its first year of operation, a theatre conference was organised by director Jim Haynes, John Calder and Kenneth Tynan. Within three years of existence, the tiny theatre club had produced 110 productions, including 28 British premieres and 33 world premieres.

At the end of the 1960s, the Traverse moved to a larger space in Edinburgh's Grassmarket, with flexible seating configurations. The first performance in this venue was on 24 Aug 1969. In its early days the theatre included exhibition space for the visual arts, until 1966 when it was taken away to establish what became the Richard Demarco Gallery.

In 1992, the Traverse moved to its current location at Cambridge Street. A £3.3 million purpose-built two theatre space with bar café was created as part of the Saltire Court development on Castle Terrace. The theatre's first performance at this location was on 3 July 1992.