Neurofibrillary tau tangles are a hallmark pathology of Alzheimer's disease (AD) and are more closely associated with AD-related cortical atrophy and symptom severity than amyloid-beta (Aβ). However, studies regarding the effect of tau on longitudinal cortical thinning, particularly in healthy aging and preclinical AD, have been limited in number due to the relatively recent introduction of in vivo PET tracers for imaging tau pathology. Here, we investigate [18F]-flortaucipir (FTP, a marker of paired helical filament tau) PET as a predictor of atrophy in healthy aging and preclinical AD. We examine longitudinal structural MRI brain imaging data, retrospectively and prospectively relative to FTP imaging, using piecewise linear mixed-effect models with time centered at each participant's FTP-PET session. Participants include 111 individuals from the Harvard Aging Brain Study who underwent at least three MRI sessions over an average of 4.46 years and one FTP-PET at the approximate midpoint of the observation period. Our primary analyses focus on inferior temporal (IT) FTP standardized uptake value ratios and longitudinal FreeSurfer defined cortical regions of interest. Relationships were also explored using other regional FTP measures (entorhinal, composite, and local), within high and low Pittsburgh compound-B (PiB) PET groups, and with longitudinal subcortical volume. Strong associations between IT FTP and cortical thinning were found, most notably in temporal, midline, and prefrontal regions, with stronger effects generally observed in the prospective as compared to retrospective time frame. Significant differences between prospective and retrospective rates of thinning were found in the inferior and middle temporal gyri, cingulate areas, as well as pars orbitalis such that higher IT FTP was associated with greater prospective rates of thinning. Within the high PiB group, significant differences between prospective and retrospective rates of thinning were similarly observed. However, no consistent pattern of tau-related change in cortical thickness within the low PiB group was discerned. These results provide support for the hypothesis that tau pathology is a driver of future atrophy as well as provide additional evidence for tau-PET as an effective AD biomarker for interventional clinical trials.