Importance: Tau positron emission tomography (PET) tracers have proven useful for the differential diagnosis of dementia, but their utility for predicting cognitive change is unclear. Objective: To examine the prognostic accuracy of baseline fluorine 18 ( 18F)-flortaucipir and [ 18F]RO948 (tau) PET in individuals across the Alzheimer disease (AD) clinical spectrum and to perform a head-to-head comparison against established magnetic resonance imaging (MRI) and amyloid PET markers. Design, Setting, and Participants: This prognostic study collected data from 8 cohorts in South Korea, Sweden, and the US from June 1, 2014, to February 28, 2021, with a mean (SD) follow-up of 1.9 (0.8) years. A total of 1431 participants were recruited from memory clinics, clinical trials, or cohort studies; 673 were cognitively unimpaired (CU group; 253 [37.6%] positive for amyloid-β [Aβ]), 443 had mild cognitive impairment (MCI group; 271 [61.2%] positive for Aβ), and 315 had a clinical diagnosis of AD dementia (315 [100%] positive for Aβ). Exposures: [ 18F]Flortaucipir PET in the discovery cohort (n = 1135) or [ 18F]RO948 PET in the replication cohort (n = 296), T1-weighted MRI (n = 1431), and amyloid PET (n = 1329) at baseline and repeated Mini-Mental State Examination (MMSE) evaluation. Main Outcomes and Measures: Baseline [ 18F]flortaucipir/[ 18F]RO948 PET retention within a temporal region of interest, MRI-based AD-signature cortical thickness, and amyloid PET Centiloids were used to predict changes in MMSE using linear mixed-effects models adjusted for age, sex, education, and cohort. Mediation/interaction analyses tested whether associations between baseline tau PET and cognitive change were mediated by baseline MRI measures and whether age, sex, and APOE genotype modified these associations. Results: Among 1431 participants, the mean (SD) age was 71.2 (8.8) years; 751 (52.5%) were male. Findings for [ 18F]flortaucipir PET predicted longitudinal changes in MMSE, and effect sizes were stronger than for AD-signature cortical thickness and amyloid PET across all participants (R 2, 0.35 [tau PET] vs 0.24 [MRI] vs 0.17 [amyloid PET]; P <.001, bootstrapped for difference) in the Aβ-positive MCI group (R 2, 0.25 [tau PET] vs 0.15 [MRI] vs 0.07 [amyloid PET]; P <.001, bootstrapped for difference) and in the Aβ-positive CU group (R 2, 0.16 [tau PET] vs 0.08 [MRI] vs 0.08 [amyloid PET]; P <.001, bootstrapped for difference). These findings were replicated in the [ 18F]RO948 PET cohort. MRI mediated the association between [ 18F]flortaucipir PET and MMSE in the groups with AD dementia (33.4% [95% CI, 15.5%-60.0%] of the total effect) and Aβ-positive MCI (13.6% [95% CI, 0.0%-28.0%] of the total effect), but not the Aβ-positive CU group (3.7% [95% CI, -17.5% to 39.0%]; P =.71). Age (t = -2.28; P =.02), but not sex (t = 0.92; P =.36) or APOE genotype (t = 1.06; P =.29) modified the association between baseline [ 18F]flortaucipir PET and cognitive change, such that older individuals showed faster cognitive decline at similar tau PET levels. Conclusions and Relevance: The findings of this prognostic study suggest that tau PET is a promising tool for predicting cognitive change that is superior to amyloid PET and MRI and may support the prognostic process in preclinical and prodromal stages of AD.