The group was founded by guitarist Manuel Göttsching, keyboardist/drummer Klaus Schulze, and bassist Hartmut Enke in 1971. All three founding members had previously played together as part of the short-lived group Eruption founded by Conrad Schnitzler. Prior to that Schnitzler and Schulze had worked together in Tangerine Dream.
A short-lived project Manuel Göttsching had in 1970 was the Steeple Chase Blues Band, which also included Hartmut Enke, Wolfgang Müller, and Volker Zibell.
Ash Ra Tempel released its self-titled debut album in June 1971. This release is considered by critics to be a classic of the genre; Schulze temporarily departed for a solo career shortly after its release. Schwingungen (1972), Seven Up (with Timothy Leary) (1972), and Join Inn (1973) are all considered key works from the band. The pop-oriented 1973 album Starring Rosi was thus named because it featured lead vocals by Rosi Mueller.
Their music is widely characterized as cosmic and atmospheric. The early albums were more psychedelic-oriented and all had one lengthy track per side: one more powerful and dramatic, the other of a more atmospheric nature. Instead of writing English lyrics, since German language was not popular in rock music at the time, Ash Ra Tempel more or less decided not to have lyrics in their songs.
A reunion concert performance with the original line-up took place in Cologne on February 28, 1973.
Later, after recording the soundtrack Le Berceau de Cristal (1975; unreleased until 1993) Ash Ra Tempel shortened its name to Ashra, making a more melodic, synthesizer-based music. In 2000 the band was reunited in the line-up of Manuel Gottsching and Klaus Schulze. The pair had previously worked together on Schulze's album In Blue.