Wireless hotspots, ie, infrastructures composed of several IEEE 802.11 access points (APs), are today the most common solution in providing Internet access to a wide and rapidly changing population of users. According to common device implementation, stations establish associations with APs based on the measured strongest Received Signal Strength Indicator level. This usually leads to an uneven distribution of users to APs, increasing the chances of local network congestion. Load balancing (LB) solutions aim at mitigating this problem controlling the distribution of users. The LB algorithms enforce stations to associate with APs that manage a low number of users and/or that have a low traffic load. Usually, LB solutions do not consider traffic priorities or they assume some a priori quality of service (QoS) configuration for users. In this study, we propose a QoS-LB solution based on the cell breathing technique with the goal of balancing the load in IEEE 802.11e Enhanced Distributed Channel Access (EDCA) Hotspots. The proposed algorithm explores the space of possible power/EDCA configurations by using a branch and bound approach that reduces the number of analyzed configurations and, hence, the time required to find the global optimal solution. The algorithm has been analytically defined and its performance evaluated through simulations and tests in a real test bed. The results prove that the proposed solution is effective in solving the optimal QoS-LB configuration problem in WiFi hotspots of average size.