Alzheimer’s disease (AD) is a serious neurological brain illness that results in the death of brain cells and the loss of mental and memory abilities in sufferers. Planning an appropriate course of treatment for AD requires early and accurate identification of the disease. We presented a novel approach to AD detection in this paper by combining the benefits of meta-heuristic optimization with deep learning. Hence, the Radial Basis Function Neural Network (RBFNN) and the Harris Hawks Optimization (HHO) algorithm are introduced to accurately detect AD using brain MRI data. The brain MRI images are acquired from the dataset, and then preprocessed to enhance quality in preparation for additional analysis. The RBFNN was trained using the preprocessed database to ascertain the pattern difference between normal and AD images. As a result, the HHO is used to tune the RBFNN hyperparameters to reduce processing requirements and increasing classification accuracy. The Python implementation of the proposed framework was verified using Alzheimer’s Disease Neuroimaging Initiative (ADNI) and the Open Access Series of Imaging Studies (OASIS). The results of the experiment demonstrated that the proposed strategy achieved very good performance on both datasets. The proposed method produced results for the ADNI dataset with 99.56% accuracy, 99.72% precision, 99.34% recall, and 99.51% f-measure. Similarly, the OASIS dataset produced results with accuracy, precision, recall, and f-measure of 99.27%, 99.05%, and 99.11%, respectively. The experimental and comparative analysis showed that the proposed technique outperformed the conventional models in terms of accuracy, precision, recall, and f-measure.