This study proposes a method based on fully convolutional neural networks (FCNs) to identify migratory birds from their songs, with the objective of recognizing which birds pass through certain areas and at what time. To determine the best FCN architecture, extensive experimentation was conducted through a grid search, exploring the optimal depth, width, and activation function of the network. The results showed that the optimal number of filters is 400 in the widest layer, with 4 convolutional blocks with maxpooling and an adaptive activation function. The proposed FCN offers a significant advantage over other techniques, as it can recognize the sound of a bird in audio of any length with an accuracy greater than 85%. Furthermore, due to its architecture, the network can detect more than one species from audio and can carry out near-real-time sound recognition. Additionally, the proposed method is lightweight, making it ideal for deployment and use in IoT devices. The study also presents a comparative analysis of the proposed method against other techniques, demonstrating an improvement of over 67% in the best-case scenario. These findings contribute to advancing the field of bird sound recognition and provide valuable insights into the practical application of FCNs in real-world scenarios.