Various machine translation (MT) studies are conducted for resource-rich languages such as English, Chinese, and others. However, research on MT for Ethiopian languages is still in its infancy due to the limited resources of Ethiopian languages. Harari is one of the languages spoken in Ethiopia, which is morphologically rich but severely lacking in computational linguistic tools. To overcome this problem, this research investigates the development of a bidirectional Harari–Amharic MT system using a deep learning approach. A total of 29,702 sentences from a bilingual parallel text corpus were collected, and various preprocessing tasks were applied to the corpus to prepare it for developing models. Deep learning models, namely long short-term memory (LSTM), bidirectional LSTM (BiLSTM), gated recurrent unit (GRU), and bidirectional GRU (BiGRU) without attention and with attention mechanisms, as well as Transformer models, are developed for bidirectional Harari–Amharic MT. Several experiments are conducted to find out the optimal values of the hyperparameters of the models. Using the optimal hyperparameters, the Transformer and BiGRU-Att models performed better than the other models, with accuracies of 95% and 93%, respectively. All the models are evaluated using the BLEU score, and the Transformer model is the best-performing model, with BLEU scores of 42.32 and 43.67 for Har2Amh and Amh2Har, respectively. Overall, the recurrent neural network variants and Transformer models are suitable for the development of MT systems for low-resource Harari–Amharic languages.