Objective To examine the cross-sectional associations between regional tau, β-amyloid (Aβ), and cortical thickness and neuropsychological function across the preclinical and clinical spectrum of Alzheimer disease (AD). Methods We included 106 participants from the Swedish Biomarkers for Identifying Neurodegenerative Disorders Early and Reliably (BioFINDER) study, of whom 33 had preclinical AD (Aβ-positive cognitively normal individuals), 25 had prodromal AD (Aβ-positive mild cognitive impairment), and 48 had probable AD dementia. All underwent [18F]flortaucipir (tau) and structural MRI (cortical thickness), and 88 of 106 underwent [18F]flutemetamol (Aβ) PET. Linear regression models adjusted for age, sex, and education were performed to examine associations between 7 regions of interest and 7 neuropsychological tests for all 3 imaging modalities. Results In preclinical AD, [18F]flortaucipir, but not [18F]flutemetamol or cortical thickness, was associated with decreased global cognition, memory, and processing speed (range standardized β = 0.35–0.52, p < 0.05 uncorrected for multiple comparisons). In the combined prodromal AD and AD dementia group, both increased [18F]flortaucipir uptake and reduced cortical thickness were associated with worse performance on a variety of neuropsychological tests (most regions of interest survived correction for multiple comparisons at p < 0.05), while increased [18F]flutemetamol uptake was specifically associated with lower scores on a delayed recall memory task (p < 0.05 uncorrected for multiple comparisons). The strongest effects for both [18F]flortaucipir and cortical thickness on cognition were found in the lateral and medial parietal cortex and lateral temporal cortex. The effect of [18F]flutemetamol on cognition was generally weaker and less region specific. Conclusion Our findings suggest that tau PET is more sensitive than Aβ PET and measures of cortical thickness for detecting early cognitive changes in preclinical AD. Furthermore, both [18F]flortaucipir PET and cortical thickness show strong cognitive correlates at the clinical stages of AD.