BACKGROUND: Air pollution exposure is one of the modifiable risk factors of cognitive decline. We aimed to test the association between exposure to several outdoor air pollutants and domain-specific cognitive performance. METHODS: In this cross-sectional study, we used data from the enrolment phase of the French CONSTANCES cohort. From the 220 000 people (aged 18-69 years) randomly recruited in the French CONSTANCES cohort, participants aged 45 years old or older (104 733 people) underwent a comprehensive cognitive assessment (verbal episodic memory, language skills, and executive functions). After exclusion of those who were not suitable for our analysis, 61 462 participants with available data were included in the analyses. We used annual mean concentrations at residential addresses, derived from land-use regression models, to assign exposure to particulate matter with aerodynamic diameters less than 2·5 μm (PM(2·5)), nitrogen dioxide (NO(2)), and black carbon. We used multiple linear regression models with different covariate adjustments to test the associations between each pollutant and cognitive outcomes. We did several sensitivity analyses, including multilevel modelling, meta-analysis by centre of recruitment, and exclusion of specific population groups. FINDINGS: We found significantly poorer cognitive function, especially on semantic fluency and domains of executive functions, with an increase in exposure to black carbon and NO(2). Exposure to PM(2·5) was mainly significant for the semantic fluency test. We found that decrease in cognitive performance with an increase of one interquartile range of exposure ranged from 1% to nearly 5%. The largest effect size (percentage decrease) for both PM(2.5) and NO(2) was found for the semantic fluency test (PM(2.5) 4·6%, 95% CI 2·1-6·9 and NO(2) 3·8%, 1·9-5·7), whereas for black carbon, the largest effect size was found for the digit symbol substitution test of the domains of executive functions (4·5%, 2·7-6·3). Monotonic and linear exposure-response associations were found between air pollution exposure and cognitive performance, starting from a low level of exposures. INTERPRETATION: Significantly poorer cognitive performance was associated with exposure to outdoor air pollution even at low levels of exposure. This highlights the importance of further efforts to reduce exposure to air pollution.