Digital twin (DT) technology provides a path for implementing cyber–physical systems (CPS) and developing smart manufacturing because they are essential tools for monitoring and controlling manufacturing processes. It is considered a vital technology in smart manufacturing and is being widely researched in academia and industry. Furthermore, the combination of DTs and immersive environments has shown great potential for integrating novel capabilities into the new generation of CPS. This research presents an architecture for implementing immersive digital twins under ISO 23247 in flexible manufacturing processes. The proposed system is based on the integration of DT technologies in conjunction with augmented reality (AR) and gesture tracking, and validation was performed in the sorting station of the MPS 500 to increase the interaction and flexibility between physical and virtual environments in real time, thus enhancing the capabilities of the DT. The methodology used for the design and implementation of the DT includes (1) general principles and requirements; (2) models with functional views based on domains and entities; (3) attributes of the observable manufacturing elements; and (4) protocols for the exchange of information between entities. The results show that the integration of these technologies improves the monitoring, control, and simulation capabilities of processes using 3D resources and immersive environments, achieving a higher level of interactivity. In addition, error detection tests were carried out, where a reduction of time was observed in the resolution of errors that may be caused by internal or external disturbances of the process, thus avoiding production delays.