Human brain function dynamically adjusts to ever-changing stimuli from the external environment. Studies characterizing brain functional reconfiguration are, nevertheless, scarce. Here, we present a principled mathematical framework to quantify brain functional reconfiguration when engaging and disengaging from a stop signal task (SST). We apply tangent space projection (a Riemannian geometry mapping technique) to transform the functional connectomes (FCs) of 54 participants and quantify functional reconfiguration using the correlation distance of the resulting tangent-FCs. Our goal was to compare functional reconfigurations in individuals at risk for alcohol use disorder (AUD). We hypothesized that functional reconfigurations when transitioning to/from a task would be influenced by family history of AUD (FHA) and other AUD risk factors. Multilinear regression models showed that engaging and disengaging functional reconfiguration were associated with FHA and recent drinking. When engaging in the SST after a rest condition, functional reconfiguration was negatively associated with recent drinking, while functional reconfiguration when disengaging from the SST was negatively associated with FHA. In both models, several other factors contributed to the functional reconfiguration. This study demonstrates that tangent-FCs can characterize task-induced functional reconfiguration and that it is related to AUD risk. Author Summary Human brain function constantly adapts to the external environment stimuli and transitions between cognitive states, which can be hindered by alcohol misuse and family history of alcohol use disorder (AUD). In this work, we used a novel methodology that applies Riemannian geometry concepts to functional connectivity to quantify functional reconfiguration of rest-to-task (engaging) and task-to-rest (disengaging) transitions. We ultimately aimed to determine the relationship between AUD risk factors and functional reconfiguration. Our findings showed that engaging functional reconfiguration was diminished in participants with a family history of AUD, whereas disengaging functional reconfiguration was diminished with greater recent drinking behavior. This study suggests that analysis of functional reconfiguration using Riemannian geometry is a promising avenue to better understand rest-to-task and task-to-rest brain transitions.