CNC five-axis machine tools, with their outstanding advantages in machining accuracy, efficiency, and adaptability, have been widely used in the machining of precision components. However, due to the numerous geometric error elements in five-axis machine tools, conventional measurement methods suffer from long measurement time and high equipment cost, thus failing to meet the widespread demand for efficient accuracy testing. In this paper, a one-installation measurement device and method for geometric errors of rotary axes of five-axis machine tools based on on-machine measurement is proposed. A stepwise identification algorithm for rotary axis geometric errors is also designed for this measurement method. The method utilizes an on-machine probe to measure the actual position of the standard workpiece fixture during the machine tool′s motion. The measured data are then compared with the theoretical values. By combining the machine tool′s spatial error model with the identification algorithm, it is possible to fully identify both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of the rotary axis. Numerical simulation results show that the proposed method can accurately identify ten geometric error elements, with identification accuracy over 95%. Experimental results demonstrate that this method significantly improves the compensation effect for angular positioning errors, with compensation accuracy increased by over 70%. To further validate its accuracy, comparative tests were conducted on the identical test specimen using the XR20 wireless rotary axis calibration device and the XL-80 laser interferometer. The results indicate that the average agreement of the identification results obtained by the two instruments exceeds 97%. The entire measurement process can be completed within 15 minutes, greatly improving measurement efficiency and providing support for further research on thermal errors. The measurement method proposed in this paper is a universal method for the geometric error measurement of rotary axes in machine tools with various sizes and configurations. It has obvious advantages in reducing the cost of measuring tools and improving measurement efficiency, and possesses good application prospects.