Precision medicine aims to individualize therapeutic strategies by accounting for the molecular, environmental, and clinical heterogeneity inherent across patient populations. The concurrent maturation of multi-omics technologies—encompassing genomics, transcriptomics, proteomics, metabolomics, epigenomics, and microbiomics—has generated unprecedented volumes of complementary biological information that, when integrated, offer a holistic molecular portrait of disease. However, the complexity, high dimensionality, and heterogeneity of multi-omics datasets render traditional analytical frameworks insufficient. Artificial intelligence (AI), encompassing machine learning (ML), deep learning (DL), graph neural networks (GNNs), and transformer architectures, has emerged as the indispensable computational engine for cross-layer omics integration, latent feature extraction, and clinically actionable insight generation. This review comprehensively examines current AI methodologies for multi-omics data integration, their translational applications in oncology, cardiovascular medicine, and rare disease genomics, and the technical, ethical, and regulatory challenges impeding clinical deployment. We further articulate a forward-looking framework for responsible, equitable AI-omics integration in next-generation precision medicine.