Neuroimaging biomarkers that distinguish between changes due to typical brain ageing and Alzheimer’s disease are valuable for determining how much each contributes to cognitive decline. Supervised machine learning models can derive multivariate patterns of brain change related to the two processes, including the Spatial Patterns of Atrophy for Recognition of Alzheimer’s Disease (SPARE-AD) and of Brain Aging (SPARE-BA) scores investigated herein. However, the substantial overlap between brain regions affected in the two processes confounds measuring them independently. We present a methodology, and associated results, towards disentangling the two. T1-weighted MRI scans of 4054 participants (48-95 years) with Alzheimer’s disease, mild cognitive impairment (MCI), or cognitively normal (CN) diagnoses from the Imaging-based coordinate SysTem for AGIng and NeurodeGenerative diseases (iSTAGING) consortium were analysed. Multiple sets of SPARE scores were investigated, in order to probe imaging signatures of certain clinically or molecularly defined sub-cohorts. First, a subset of clinical Alzheimer’s disease patients (n = 718) and age- and sex-matched CN adults (n = 718) were selected based purely on clinical diagnoses to train SPARE-BA1 (regression of age using CN individuals) and SPARE-AD1 (classification of CN versus Alzheimer’s disease) models. Second, analogous groups were selected based on clinical and molecular markers to train SPARE-BA2 and SPARE-AD2 models: amyloid-positive Alzheimer’s disease continuum group (n = 718; consisting of amyloid-positive Alzheimer’s disease, amyloid-positive MCI, amyloid- and tau-positive CN individuals) and amyloid-negative CN group (n = 718). Finally, the combined group of the Alzheimer’s disease continuum and amyloid-negative CN individuals was used to train SPARE-BA3 model, with the intention to estimate brain age regardless of Alzheimer’s disease-related brain changes. The disentangled SPARE models, SPARE-AD2 and SPARE-BA3, derived brain patterns that were more specific to the two types of brain changes. The correlation between the SPARE-BA Gap (SPARE-BA minus chronological age) and SPARE-AD was significantly reduced after the decoupling (r = 0.56-0.06). The correlation of disentangled SPARE-AD was non-inferior to amyloid- and tau-related measurements and to the number of APOE ε4 alleles but was lower to Alzheimer’s disease-related psychometric test scores, suggesting the contribution of advanced brain ageing to the latter. The disentangled SPARE-BA was consistently less correlated with Alzheimer’s disease-related clinical, molecular and genetic variables. By employing conservative molecular diagnoses and introducing Alzheimer’s disease continuum cases to the SPARE-BA model training, we achieved more dissociable neuroanatomical biomarkers of typical brain ageing and Alzheimer’s disease.