In the context of fast-growing digitization of industrial environments, Industry 4.0 aims to improve key elements to achieve more efficient processes, flexibility in customizing products and reduction in energy consumption, among other objectives. This paper presents a system that exploits the Internet of Things (IoT), massive data computation, and human-robot collaboration to reach these goals. The described system combines technological and human-centered aspects to enhance human-robot interaction. In fact, the human factor cannot be left aside when technological advances affecting society are foreseen. The proposal has been tested on a gesture control system that enables a natural interaction with a robotic arm through the use of IoT-oriented inertial measurement unit devices. These devices capture the movements of both human’s arms. Experiments of a technical nature have been run to measure accuracy and latency. In addition, human-centered tests have been conducted with real users to determine the level of intuitiveness and acceptance of the proposed gesture control. The results obtained demonstrate that the proposal meets the demands in terms of real-time, success rate, flexibility and scalability, which are fundamental requirements in Industry 4.0. The usability results have enabled drawing useful conclusions on the use of such human-robot interaction systems.