In this paper, we investigate the problem of allocating energy-efficient transmission and computation resources for federated learning (FL) across wireless communication networks. In the FL model we investigate, each user computes limited local computational resources to train a local FL model with its collected data. Subsequently, the trained FL model is sent to a base station (BS), which aggregates the local FL models and broadcasts the resulting model back to all users. Because FL entails exchanging a learning model between users and the BS, computation, and communication latencies are contingent on the level of learning accuracy. Additionally, due to the wireless users’ constrained energy budgets, we should consider both local computation energy and transmission energy during the FL process. We formulate the challenge of learning process and communication as an optimization task to minimize the overall energy consumption of the system while adhering to a latency constraint. To address this problem, we investigate an iterative algorithm wherein closed-form solutions for resource allocation with latency, bandwidth, transmit power, computation frequency, and learning accuracy are derived at each step. Given that the iterative algorithm necessitates an initial feasible solution, we apply a deep reinforcement learning (DRL)-based algorithm. The results demonstrate our work can reduce total energy consumption by up to 65% compared to other DRL agents.