Alzheimer's disease is a progressive neurodegenerative disorder that poses a growing global public health challenge. Early and accurate diagnosis is critical for effective treatment, clinical trial participation, and disease management. This systematic review and meta-analysis evaluates the diagnostic performance of machine learning (ML) and deep learning (DL) algorithms for detecting Alzheimer's disease (AD) and mild cognitive impairment (MCI) using neuroimaging and clinical data. Relevant studies were identified from PubMed, IEEE Xplore, and arXiv (2015 to 2025). Random-effects models were applied to estimate pooled performance metrics (AUC, sensitivity, specificity, and F1-score), and subgroup analyses compared results by model type, imaging modality, and validation strategy. Thirty studies met inclusion criteria. The pooled AUC was 0.962, indicating high overall discriminative accuracy. However, studies relying solely on internal validation or with smaller datasets often reported inflated metrics, suggesting potential overfitting and optimism bias. ML and DL methods demonstrate strong potential for early AD detection, but standardized evaluation protocols and external validation are necessary for clinical translation.