Scylla is a deep Hubble Space Telescope (HST) survey of the stellar populations, interstellar medium, and star formation in the LMC and SMC. As a pure-parallel complement to the Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) survey, Scylla obtained 342 orbits of ultraviolet (UV) through near-IR imaging of the LMC and SMC with Wide Field Camera 3. In this paper, we describe the science objectives, observing strategy, data reduction procedure, and initial results from our photometric analysis of 96 observed fields. Although our observations were constrained by ULLYSES primary exposures, we imaged all fields in at least two filters (F475W and F814W) and 64% of fields in at least three and as many as seven WFC3 filters spanning the UV to IR. Overall, we reach average 50% completeness of m_F225W_=26.0, m_F275W_=26.2, m_F336W_=26.9, m_F475W_=27.8, m_F814W_=25.5, m_F110W_=24.7, and m_F160W_=24.0 Vega mag in our photometric catalogs, which is faintward of the ancient main-sequence turnoff in all filters. The primary science goals of Scylla include characterizing the structure and properties of dust in the MCs, as well as their spatially resolved star formation and chemical enrichment histories. Our images and photometric catalogs, which represent the widest-area coverage of MCs with HST photometry to date, are available as a high-level science product at the Barbara A. Mikulski Archive for Space Telescopes.