In this paper we propose an energy-aware broadcast algorithm for wireless networks. Our algorithm is based on the multicost approach and selects the set of nodes that by transmitting implement broadcasting in an optimally energy-efficient way. The energy-related parameters taken into account are the node transmission power and the node residual energy. The algorithmâ€™s complexity however is non-polynomial, and therefore, we propose a relaxation producing a near-optimal solution in polynomial time. We also consider a distributed information exchange scheme that can be coupled with the proposed algorithms and examine the overhead introduced by this integration. Using simulations we show that the proposed algorithms outperform other solutions in the literature in terms of energy efficiency. Moreover, it is shown that the near-optimal algorithm obtains most of the performance benefits of the optimal algorithm at a smaller computational overhead.