Background: Changes in grey matter covariance networks have been reported in preclinical and clinical stages of Alzheimer’s disease (AD) and have been associated with amyloid-β (Aβ) deposition and cognitive decline. However, the role of tau pathology on grey matter networks remains unclear. Based on previously reported associations between tau pathology, synaptic density and brain structural measures, tau-related connectivity changes across different stages of AD might be expected. We aimed to assess the relationship between tau aggregation and grey matter network alterations across the AD continuum. Methods: We included 533 individuals (178 Aβ-negative cognitively unimpaired (CU) subjects, 105 Aβ-positive CU subjects, 122 Aβ-positive patients with mild cognitive impairment, and 128 patients with AD dementia) from the BioFINDER-2 study. Single-subject grey matter networks were extracted from T1-weighted images and graph theory properties including degree, clustering coefficient, path length, and small world topology were calculated. Associations between tau positron emission tomography (PET) values and global and regional network measures were examined using linear regression models adjusted for age, sex, and total intracranial volume. Finally, we tested whether the association of tau pathology with cognitive performance was mediated by grey matter network disruptions. Results: Across the whole sample, we found that higher tau load in the temporal meta-ROI was associated with significant changes in degree, clustering, path length, and small world values (all p < 0.001), indicative of a less optimal network organisation. Already in CU Aβ-positive individuals associations between tau burden and lower clustering and path length were observed, whereas in advanced disease stages elevated tau pathology was progressively associated with more brain network abnormalities. Moreover, the association between higher tau load and lower cognitive performance was only partly mediated (9.3 to 9.5%) through small world topology. Conclusions: Our data suggest a close relationship between grey matter network disruptions and tau pathology in individuals with abnormal amyloid. This might reflect a reduced communication between neighbouring brain areas and an altered ability to integrate information from distributed brain regions with tau pathology, indicative of a more random network topology across different AD stages.