Ensemble clustering, a paradigm that deals with combining the results of multiple clusterings into a single solution, has been widely studied in recent years. The goal of this study is to propose a novel distributed ensemble clustering method that is applicable for use in networked multi-agent systems. The adopted setting supports both object-distributed and feature-distributed clusterings. It is not limited to specific types of algorithms used for obtaining local data labels. The method assumes local processing of local data by the individual agents and neighbor-wise communication of the processed information between the neighboring agents in the network. Using the proposed communication scheme, all agents are able to achieve reliable global results in a fully decentralized way. The network communication design is based on the multi-agent consensus averaging algorithm applied to clustering similarity matrices. It provably results in the fastest convergence to the desired asymptotic values. Several simulation examples illustrate the performance of the proposed distributed solution in different scenarios, including diverse datasets, networks, and applications within the multimedia domain. They show that the obtained performance is very close to that of the corresponding centralized solution.