The Asteroid Terrestrial impact Last Alert System (ATLAS) system consists of two 0.5 m Schmidt telescopes with cameras covering 29 square degrees at plate scale of 1.86 arcsec per pixel. Working in tandem, the telescopes routinely survey the whole sky visible from Hawaii (above delta > -50 degrees) every two nights, exposing four times per night, typically reaching o < 19 magnitude per exposure when the moon is illuminated and c < 19.5 magnitude per exposure in dark skies. Construction is underway of two further units to be sited in Chile and South Africa which will result in an all-sky daily cadence from 2021. Initially designed for detecting potentially hazardous near earth objects, the ATLAS data enable a range of astrophysical time domain science. To extract transients from the data stream requires a computing system to process the data, assimilate detections in time and space and associate them with known astrophysical sources. Here we describe the hardware and software infrastructure to produce a stream of clean, real, astrophysical transients in real time. This involves machine learning and boosted decision tree algorithms to identify extragalactic and Galactic transients. Typically we detect 10-15 supernova candidates per night which we immediately announce publicly. The ATLAS discoveries not only enable rapid follow-up of interesting sources but will provide complete statistical samples within the local volume of 100 Mpc. A simple comparison of the detected supernova rate within 100 Mpc, with no corrections for completeness, is already significantly higher (factor 1.5 to 2) than the current accepted rates.