Magnetic influences increase in importance in the solar atmosphere from the photosphere out into the corona, yet our ability to routinely measure magnetic fields in the outer solar atmosphere is lacking. We describe the scientific objectives and capabilities of the COronal Solar Magnetism Observatory (COSMO), a proposed synoptic facility designed to measure magnetic fields and plasma properties in the large‐scale solar atmosphere. COSMO comprises a suite of three instruments chosen to enable the study of the solar atmosphere as a coupled system: (1) a coronagraph with a 1.5 m aperture to measure the magnetic field, temperature, density, and dynamics of the corona; (2) an instrument for diagnostics of chromospheric and prominence magnetic fields and plasma properties; and (3) a white light K‐coronagraph to measure the density structure and dynamics of the corona and coronal mass ejections. COSMO will provide a unique combination of magnetic field, density, temperature, and velocity observations in the corona and chromosphere that have the potential to transform our understanding of fundamental physical processes in the solar atmosphere and their role in the origins of solar variability and space weather. Key Points Society is becoming increasingly vulnerable to the effects of space weather The physical processes responsible for solar activity remain poorly understood COSMO will provide key measurements to advance our understanding of solar processes and activity