Tau pathology, neuroinflammation, and neurodegeneration are key aspects of Alzheimer's disease. Understanding whether these features predict cognitive decline, alone or in combination, is crucial to develop new prognostic measures and enhanced stratification for clinical trials. Here, we studied how baseline assessments of in vivo tau pathology (measured by 18F-AV-1451 PET), neuroinflammation (measured by 11C-PK11195 PET) and brain atrophy (derived from structural MRI) predicted longitudinal cognitive changes in patients with Alzheimer's disease pathology. Twenty-six patients (n = 12 with clinically probable Alzheimer's dementia and n = 14 with amyloid-positive mild cognitive impairment) and 29 healthy control subjects underwent baseline assessment with 18F-AV-1451 PET, 11C-PK11195 PET, and structural MRI. Cognition was examined annually over the subsequent 3 years using the revised Addenbrooke's Cognitive Examination. Regional grey matter volumes, and regional binding of 18F-AV-1451 and 11C-PK11195 were derived from 15 temporo-parietal regions characteristically affected by Alzheimer's disease pathology. A principal component analysis was used on each imaging modality separately, to identify the main spatial distributions of pathology. A latent growth curve model was applied across the whole sample on longitudinal cognitive scores to estimate the rate of annual decline in each participant. We regressed the individuals' estimated rate of cognitive decline on the neuroimaging components and examined univariable predictive models with single-modality predictors, and a multi-modality predictive model, to identify the independent and combined prognostic value of the different neuroimaging markers. Principal component analysis identified a single component for the grey matter atrophy, while two components were found for each PET ligand: one weighted to the anterior temporal lobe, and another weighted to posterior temporo-parietal regions. Across the whole-sample, the single-modality models indicated significant correlations between the rate of cognitive decline and the first component of each imaging modality. In patients, both stepwise backward elimination and Bayesian model selection revealed an optimal predictive model that included both components of 18F-AV-1451 and the first (i.e. anterior temporal) component for 11C-PK11195. However, the MRI-derived atrophy component and demographic variables were excluded from the optimal predictive model of cognitive decline. We conclude that temporo-parietal tau pathology and anterior temporal neuroinflammation predict cognitive decline in patients with symptomatic Alzheimer's disease pathology. This indicates the added value of PET biomarkers in predicting cognitive decline in Alzheimer's disease, over and above MRI measures of brain atrophy and demographic data. Our findings also support the strategy for targeting tau and neuroinflammation in disease-modifying therapy against Alzheimer's disease.