Air Turbine Starter (ATS) systems are provided, as gas turbine engines including ATS systems. In one embodiment, a gas turbine engine includes an accessory gearbox (AGB) and an integrated Air Turbine Starter (ATS) system. The AGB includes a gearbox gear train within a gearbox housing. The integrated ATS system is removably installed on the AGB and includes an ATS having an air turbine and an output shaft coupled thereto. An ATS clutch module is coupled to the ATS output shaft. The ATS clutch module is further within the gearbox housing and mechanically couples the ATS output shaft to the gearbox gear train when the integrated ATS system is installed on the AGB.