Nearly 75% of older adults in the United States report balance problems. Balance difficulties are more pronounced during sensory feedback perturbation (e.g., standing with the eyes closed or on foam). Although it is known that aging results in widespread brain atrophy, less is known about how brain structure relates to balance performance under varied sensory conditions in older age. We measured postural sway of 36 young (18-34 years) and 22 older (66-84 years) adults during four conditions: eyes open, eyes closed, eyes open on foam, and eyes closed on foam. We calculated three summary measures indicating visual, proprioceptive, and vestibular contributions to balance. We also collected T1-weighted and diffusion-weighted anatomical MRI scans. We aimed to: 1) test for age group differences in brain structure-balance relationships across a range of structural brain measures (i.e., volumetric, surface, and white matter microstructure); and 2) assess how brain structure measures relate to balance, regardless of age. Across both age groups, thinner cortex in multisensory integration regions was associated with greater reliance on visual inputs for balance. Greater gyrification within sensorimotor and parietal cortices was associated with greater reliance on proprioceptive inputs for balance. Poorer vestibular function was correlated with thinner vestibular cortex, greater gyrification within sensorimotor, parietal, and frontal cortices, and lower free water-corrected axial diffusivity in the superior-posterior corona radiata and across the corpus callosum. These results contribute to our scientific understanding of how individual differences in brain structure relate to balance. This has implications for developing brain stimulation interventions to improve balance.