Alzheimer's disease (AD), characterized by progressive cognitive decline and memory loss, presents a formidable global health challenge, underscoring the critical importance of early and precise diagnosis for timely interventions and enhanced patient outcomes. While MRI scans provide valuable insights into brain structures, traditional analysis methods often struggle to discern intricate 3D patterns crucial for AD identification. Addressing this challenge, we introduce an alternative end-to-end deep learning model, the 3D Hybrid Compact Convolutional Transformers 3D (HCCT). By synergistically combining convolutional neural networks (CNNs) and vision transformers (ViTs), the 3D HCCT adeptly captures both local features and long-range relationships within 3D MRI scans. Extensive evaluations on prominent AD benchmark dataset, ADNI, demonstrate the 3D HCCT's superior performance, surpassing state of the art CNN and transformer-based methods in classification accuracy. Its robust generalization capability and interpretability marks a significant stride in AD classification from 3D MRI scans, promising more accurate and reliable diagnoses for improved patient care and superior clinical outcomes.