The spectrum, pathophysiology, and recovery trajectory of persistent post-COVID-19 cognitive deficits are unknown, limiting our ability to develop prevention and treatment strategies. We report the one-year cognitive, serum biomarker, and neuroimaging findings from a prospective, national study of cognition in 351 COVID-19 patients who had required hospitalisation, compared to 2,927 normative matched controls. Cognitive deficits were global and associated with elevated brain injury markers, and reduced anterior cingulate cortex volume one year after COVID-19. The severity of the initial infective insult, post-acute psychiatric symptoms, and a history of encephalopathy were associated with greatest deficits. There was strong concordance between subjective and objective cognitive deficits. Longitudinal follow-up in 106 patients demonstrated a trend toward recovery. Together, these findings support the hypothesis that brain injury in moderate to severe COVID-19 may be immune-mediated, and should guide the development of therapeutic strategies.