We introduce GENomic Encoding REpresentation with Language Model (GENEREL), a framework designed to bridge genetic and biomedical knowledge bases. What sets GENEREL apart is its ability to fine-tune language models to infuse biological knowledge behind clinical concepts such as diseases and medications. This fine-tuning enables the model to capture complex biomedical relationships more effectively, enriching the understanding of how genomic data connects to clinical outcomes. By constructing a unified embedding space for biomedical concepts and a wide range of common SNPs from sources such as patient-level data, biomedical knowledge graphs, and GWAS summaries, GENEREL aligns the embeddings of SNPs and clinical concepts through multi-task contrastive learning. This allows the model to adapt to diverse natural language representations of biomedical concepts while bypassing the limitations of traditional code mapping systems across different data sources. Our experiments demonstrate GENEREL's ability to effectively capture the nuanced relationships between SNPs and clinical concepts. GENEREL also emerges to discern the degree of relatedness, potentially allowing for a more refined identification of concepts. This pioneering approach in constructing a unified embedding system for both SNPs and biomedical concepts enhances the potential for data integration and discovery in biomedical research.