In Wireless mesh networks mesh access points (MAPs) forward traffic wirelessly towards users or Internet gateways. A user device usually connects to the MAP with the strongest signal, as such MAP should guarantee the best quality of service. However, this connection policy may lead to: (i) unfairness towards users that are distant from gateways; (ii) uneven distribution of users to MAPs; and (iii) inefficient use of network paths. We present a new model and solution approach to the problem of assigning users to MAPs and routing the data within the mesh network with the objective of providing max-min fair throughput. The problem is formulated as a mixed-integer linear programming problem (MILP). Because of the inherent complexity of the problem, real size instances cannot be solved to optimality within the time limits for online optimization. Therefore, we propose an original heuristic solution algorithm for the resulting MILP. Both numerical comparisons and network simulations demonstrate the effectiveness of the proposed heuristic. For random networks, the heuristic achieves 98% of the optimal solution. Network simulations show that in medium-sized networks, the number of users with at least 1 Mbit/s minimum end-to-end rate increases by 550% when compared with the classical signal-strength based association.