The underutilized millimeter-wave (mm-wave) band is a promising candidate to enable extremely high data rate communications in future wireless networks. However, the special characteristics of the mm-wave systems such as high vulnerability to obstacles (due to high penetration loss) and to mobility (due to directional communications) demand a careful design of the association between the clients and access points (APs). This challenge can be addressed by distributed association techniques that gracefully adapt to wireless channel variations and client mobilities. We formulated the association problem as a mixed-integer optimization aiming to maximize the network throughput with proportional fairness guarantees. This optimization problem is solved first by a distributed dual decomposition algorithm, and then by a novel distributed auction algorithm where the clients act asynchronously to achieve near-to-optimal association between the clients and APs. The latter algorithm has a faster convergence with a negligible drop in the resulting network throughput. A distinguishing novel feature of the proposed algorithms is that the resulting optimal association does not have to be re-computed every time the network changes (e.g., due to mobility). Instead, the algorithms continuously adapt to the network variations and are thus very efficient. We discuss the implementation of the proposed algorithms on top of existing communication standards. The numerical analysis verifies the ability of the proposed algorithms to optimize the association and to maintain optimality in the time-variant environments of the mm-wave networks.