BACKGROUND: Spain is one of the European countries most affected by the COVID-19 pandemic. Serological surveys are a valuable tool to assess the extent of the epidemic, given the existence of asymptomatic cases and little access to diagnostic tests. This nationwide population-based study aims to estimate the seroprevalence of SARS-CoV-2 infection in Spain at national and regional level. METHODS: 35 883 households were selected from municipal rolls using two-stage random sampling stratified by province and municipality size, with all residents invited to participate. From April 27 to May 11, 2020, 61 075 participants (75.1% of all contacted individuals within selected households) answered a questionnaire on history of symptoms compatible with COVID-19 and risk factors, received a point-of-care antibody test, and, if agreed, donated a blood sample for additional testing with a chemiluminescent microparticle immunoassay. Prevalences of IgG antibodies were adjusted using sampling weights and post-stratification to allow for differences in non-response rates based on age group, sex, and census-tract income. Using results for both tests, we calculated a seroprevalence range maximising either specificity (positive for both tests) or sensitivity (positive for either test). FINDINGS: Seroprevalence was 5.0% (95% CI 4.7-5.4) by the point-of-care test and 4.6% (4.3-5.0) by immunoassay, with a specificity-sensitivity range of 3.7% (3.3-4.0; both tests positive) to 6.2% (5.8-6.6; either test positive), with no differences by sex and lower seroprevalence in children younger than 10 years (<3.1% by the point-of-care test). There was substantial geographical variability, with higher prevalence around Madrid (>10%) and lower in coastal areas (<3%). Seroprevalence among 195 participants with positive PCR more than 14 days before the study visit ranged from 87.6% (81.1-92.1; both tests positive) to 91.8% (86.3-95.3; either test positive). In 7273 individuals with anosmia or at least three symptoms, seroprevalence ranged from 15.3% (13.8-16.8) to 19.3% (17.7-21.0). Around a third of seropositive participants were asymptomatic, ranging from 21.9% (19.1-24.9) to 35.8% (33.1-38.5). Only 19.5% (16.3-23.2) of symptomatic participants who were seropositive by both the point-of-care test and immunoassay reported a previous PCR test. INTERPRETATION: The majority of the Spanish population is seronegative to SARS-CoV-2 infection, even in hotspot areas. Most PCR-confirmed cases have detectable antibodies, but a substantial proportion of people with symptoms compatible with COVID-19 did not have a PCR test and at least a third of infections determined by serology were asymptomatic. These results emphasise the need for maintaining public health measures to avoid a new epidemic wave. FUNDING: Spanish Ministry of Health, Institute of Health Carlos III, and Spanish National Health System.