Systems for determining the position of objects inside buildings have a wide range of applications, such as the surveillance of people’s movements in hospitals, and of goods or mobile robots in warehouse spaces or production halls. Hence, there is a need for the development of methods that could be applied for those purposes. This paper presents the results of research on an experimental system for localizing people being evacuated from a building. The proposed solution was designed as a part of the building evacuation management system. The method used for finding location belongs to the class of proximity-type methods and is based on Received Signal Strength Indicator (RSSI) information of Bluetooth Low-Energy (BLE) devices. The devices used to build the system (BLE receivers) and the evacuee’s wristband (BLE transmitters) are low-budget electronic modules. The paper presents preliminary research and the process of selecting data processing methods, as well as the results of tests of the experimental network created for the evacuation system. The results of measurements and statistical analyses of the properties of the RSSI parameter of the BLE signal transmission between the modules used in the designed system are presented. In addition, the results of RSSI measurements and the analyses of RSSI recorded under varying environmental conditions in the building are presented. The choice of the data processing method and its parameters was made with the use of the determined probabilities of the nearest locator node detection. Finally, the performance of the experimental installation of the evacuee tracking system was tested and the effectiveness of the proximity method was evaluated. The experimental tests aimed to analyze the detection range and the impact of shading. They also allowed for determining the mean error and for estimating the maximum position determination error. It should be emphasized that the proposed position estimation method has a very low computational load, allowing the implementation of an extensive real-time system on a typical personal computer. Although the proposed system should be classified as a coarse positioning system, its features such as low cost, simplicity, flexibility, the use of commonly available components and low requirements for computational load make it attractive. Such a system is directly transferable to other applications in, for example, Industry 4.0.