Characterizing Alzheimer’s disease (AD) at pre-clinical stages is crucial for initiating early treatment strategies. It is widely accepted that amyloid accumulation is a primary pathological event in AD. Also, loss of connectivity between brain regions is suspected of contributing to cognitive decline, but studies that test these associations using either local (i.e., individual edges) or global (i.e., modularity) connectivity measures may be limited. In this study, we utilized data acquired from 139 cognitively unimpaired participants. Sixteen gray matter (GM) regions known to be affected by AD were selected for analysis. For each of the 16 regions, the effect of amyloid burden, measured using Pittsburgh Compound B (PiB) positron emission tomography, on each of the 1761 brain network connections derived from diffusion tensor imaging (DTI) connecting 162 GM regions, was investigated. Applying our unique multiresolution statistical analysis called the Wavelet Connectivity Signature (WaCS), this study demonstrates the relationship between amyloid burden and structural brain connectivity as assessed with DTI. Our statistical analysis using WaCS shows that in 15 of 16 GM regions, statistically significant relationships between amyloid burden in those regions and structural connectivity networks were observed. After applying multiple testing correction, 10 unique structural brain connections were found to be significantly associated with amyloid accumulation. For 7 of those 10 network connections, the decrease in their network connection strength indexed by fractional anisotropy was, in turn, associated with lower cognitive function, providing evidence that AD-related structural connectivity loss is a correlate of cognitive decline.