Introduction Published reports of associations between β‐amyloid (Aβ) and cortical integrity conflict. Tau biomarkers may help elucidate the complex relationship between pathology and neurodegeneration in aging. Methods We measured cortical thickness using magnetic resonance imaging, Aβ using Pittsburgh compound B positron emission tomography (PiB‐PET), and tau using flortaucipir (FTP)‐PET in 125 cognitively normal older adults. We examined relationships among PET measures, cortical thickness, and cognition. Results Cortical thickness was reduced in PiB+/FTP+ participants compared to the PiB+/FTP– and PiB–/FTP– groups. Continuous PiB associations with cortical thickness were weak but positive in FTP– participants and negative in FTP+. FTP strongly negatively predicted thickness regardless of PiB status. FTP was associated with memory and cortical thickness, and mediated the association of PiB with memory. Discussion Past findings linking Aβ and cortical thickness are likely weak due to opposing effects of Aβ on cortical thickness relative to tau burden. Tau, in contrast to Aβ, is strongly related to cortical thickness and memory.