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In this paper, we propose a new algorithm for distributed spectrum sensing and channel selection in cognitive radio networks based on consensus. The algorithm operates within a multi-agent reinforcement learning scheme. The proposed consensus strategy, implemented over a directed, typically sparse, time-varying low-bandwidth communication network, enforces collaboration between the agents in a completely decentralized and distributed way. The motivation for the proposed approach comes directly from typical cognitive radio networks' practical scenarios, where such a decentralized setting and distributed operation is of essential importance. Specifically, the proposed setting provides all the agents, in unknown environmental and application conditions, with viable network-wide information. Hence, a set of participating agents becomes capable of successful calculation of the optimal joint spectrum sensing and channel selection strategy even if the individual agents are not. The proposed algorithm is, by its nature, scalable and robust to node and link failures. The paper presents a detailed discussion and analysis of the algorithm's characteristics, including the effects of denoising, the possibility of organizing coordinated actions, and the convergence rate improvement induced by the consensus scheme. The results of extensive simulations demonstrate the high effectiveness of the proposed algorithm, and that its behavior is close to the centralized scheme even in the case of sparse neighbor-based inter-node communication. [ABSTRACT FROM AUTHOR]