Automatic modulation classification (AMC) plays a vital role in modern wireless communication systems by enabling efficient spectrum utilization and ensuring reliable data transmission. With increasing complexity in communication signals, traditional AMC methods face challenges in accurately classifying modulation types, particularly when deployed in cloud-based environments with scalable resources. This study aims to develop a robust AMC method that leverages deep learning-derived features combined with an optimized Extreme Learning Machine (ELM) classifier to enhance classification accuracy and reliability. Features are extracted using pre-trained deep learning models-Inception V3, ResNet 50, and VGG 16-and concatenated into a comprehensive feature set. These features are input into an ELM whose hidden-node parameters are optimized via the Moth Flame Optimization (MFO) algorithm, resulting in the MFOP-ELM classifier. Additionally, explainable AI techniques, including SHAP value analysis, are applied to interpret model predictions. The approach is evaluated on three cloud-based virtual machines with configurations of vCPU-4/16GB RAM, vCPU-8/32GB RAM, and vCPU-16/64GB RAM. The proposed MFOP-ELM model achieves a classification accuracy of 94.19%, sensitivity of 89.56%, and specificity of 88.76% on the highest configuration (vCPU-16/64GB RAM). Performance comparisons demonstrate that this method outperforms existing state-of-the-art AMC approaches. The integration of deep learning features with an MFO-optimized ELM classifier provides a highly accurate and interpretable solution for automatic modulation classification, effective in both cloud and standalone environments.