The Deep Extragalactic VIsible Legacy Survey (DEVILS) is a large spectroscopic campaign at the Anglo-Australian Telescope (AAT) aimed at bridging the near and distant Universe by producing the highest completeness survey of galaxies and groups at intermediate redshifts (0.3 <z <1.0). Our sample consists of similar to 60 000 galaxies to Y <21.2 mag, over similar to 6 deg(2) in three well-studied deep extragalactic fields (Cosmic Origins Survey field, COSMOS; Extended Chandra Deep Field South, ECDFS; and the X-ray Multi-Mirror Mission Large-Scale Structure region, XMM-LSS - all Large Synoptic Survey Telescope deep-drill fields). This paper presents the broad experimental design of DEVILS. Our target sample has been selected from deep Visible and Infrared Survey Telescope for Astronomy (VISTA) Y-band imaging (VISTA Deep Extragalactic Observations, VIDEO and UltraVISTA), with photometry measured by PROFOUND. Photometric star/galaxy separation is done on the basis of near-infrared colours and has been validated by visual inspection. To maximize our observing efficiency for faint targets, we employ a redshift feedback strategy, which continually updates our target lists, feeding back the results from the previous night's observations. We also present an overview of the initial spectroscopic observations undertaken in late 2017 and early 2018.