We describe plans for the development of the Southern Wide-field Gamma-ray Observatory (SWGO), a next-generation instrument with sensitivity to the very-high-energy (VHE) band to be constructed in the Southern Hemisphere. SWGO will provide wide-field coverage of a large portion of the southern sky, effectively complementing current and future instruments in the global multi-messenger effort to understand extreme astrophysical phenomena throughout the universe. A detailed description of science topics addressed by SWGO is available in the science case white paper [1]. The development of SWGO will draw on extensive experience within the community in designing, constructing, and successfully operating wide-field instruments using observations of extensive air showers. The detector will consist of a compact inner array of particle detection units surrounded by a sparser outer array. A key advantage of the design of SWGO is that it can be constructed using current, already proven technology. We estimate a construction cost of 54M USD and a cost of 7.5M USD for 5 years of operation, with an anticipated US contribution of 20M USD ensuring that the US will be a driving force for the SWGO effort. The recently formed SWGO collaboration will conduct site selection and detector optimization studies prior to construction, with full operations foreseen to begin in 2026. Throughout this document, references to science white papers submitted to the Astro2020 Decadal Survey with particular relevance to the key science goals of SWGO, which include unveiling Galactic particle accelerators [2-10], exploring the dynamic universe [11-21], and probing physics beyond the Standard Model [22-25], are highlighted in red boldface.