The present paper develops a decentralized expectation-maximization (EM) algorithm to estimate the parameters of a mixture density model for use in distributed learning tasks performed with data collected at spatially deployed wireless sensors. The E-step in the novel iterative scheme relies on local information available to individual sensors, while during the M-step sensors exchange information only with their one- hop neighbors to reach consensus and eventually percolate the global information needed to estimate the wanted parameters across the wireless sensor network (WSN). Analysis and simulations demonstrate that the resultant consensus-based distributed EM (CB-DEM) algorithm matches well the resource- limited characteristics of WSNs and compares favorably with existing alternatives because it has wider applicability and remains resilient to inter-sensor communication noise.