Aging is associated with declines in cognition and brain structural integrity. However, there is equivocality over (1) the specificity of affected domains in different people, (2) the location of associated patterns of brain structural deterioration, and (3) the sociodemographic factors contributing to ‘unhealthy’ cognition. We aimed to identify cognitive profiles displayed by older adults and determine brain and sociodemographic features potentially shaping these profiles. A sample of Southeast-Asian older adults (N = 386) participated in a multi-session study comprising cognitive testing, neuroimaging, and a structured interview. We used computational models to extract latent mechanisms underlying cognitive flexibility and response inhibition. Data-driven methods were used to construct cognitive profiles based on standard performance measures and model parameters. We also investigated grey matter volume and machine-learning derived ‘brain-ages’. A profile associated with poor set-shifting and rigid focusing was associated with widespread grey matter reduction in cognitive control regions. A slow responding profile was associated with advanced brain-age. Both profiles were correlated with poor socioeconomic standing and cognitive reserve. We found that the impact of sociodemographic factors on cognitive profiles was partially mediated by total grey and white matter, and dorsolateral prefrontal and cerebellar volumes. This study furthers understanding of how distinct aging profiles of cognitive impairment uniquely correspond to specific vs. global brain deterioration and the significance of socioeconomic factors in informing cognitive performance in older age.