IoT devices play an integral part of our digital life today, yet pose significant security risks. These risks allow attackers to carry out various cyberattacks, mainly distributed denial of service (DDoS) attacks. To address these challenges, this paper proposes a hybrid deep learning approach that uses deep neural networks (DNNs) and long short-term memory (LSTM) networks to classify IoT cybersecurity attacks. The binary classification technique of LSTM is applied, whereby the models indicated sufficient results in terms of accuracy and performance, with the LSTM model showing an accuracy of 0.999 and the DNN model showing an accuracy of 0.999. To enhance detection capabilities, we used a comprehensive approach that includes 15 different attack categories. Although the DNN model equals the LSTM model with an accuracy of 0.95 in some scenarios, the hybrid model, which integrates the DNN feature outputs and the LSTM-derived features, showed an overall accuracy of 95.36. We further conducted extensive tests on the Edge-IIoT dataset to validate the effectiveness of our hybrid model. The proposed solution effectively exploits the strengths of the DNN and LSTM architectures, providing a robust framework for detecting and classifying DDoS attacks within IoT networks. These results contribute to a promising approach to mitigate the risks associated with IoT vulnerabilities.