Although the Greater Caucasus Mountains have played a central role in absorbing late Cenozoic convergence between the Arabian and Eurasian plates, the orogenic architecture and the ways in which it accommodates modern shortening remain debated. Here, we addressed this problem using geologic mapping along two transects across the southern half of the western Greater Caucasus to reveal a suite of regionally coherent stratigraphic packages that are juxtaposed across a series of thrust faults, which we call the North Georgia fault system. From south to north within this system, stratigraphically repeated ~5–10-km-thick thrust sheets show systematically increasing bedding dip angles (<30° in the south to subvertical in the core of the range). Likewise, exhumation depth increases toward the core of the range, based on low-temperature thermochronologic data and metamorphic grade of exposed rocks. In contrast, active shortening in the modern system is accommodated, at least in part, by thrust faults along the southern margin of the orogen. Facilitated by the North Georgia fault system, the western Greater Caucasus Mountains broadly behave as an in-sequence, southward-propagating imbricate thrust fan, with older faults within the range progressively abandoned and new structures forming to accommodate shortening as the thrust propagates southward. We suggest that the single-fault-centric “Main Caucasus thrust” paradigm is no longer appropriate, as it is a system of faults, the North Georgia fault system, that dominates the architecture of the western Greater Caucasus Mountains.