Bio-ontologies and Linked Data have become integral part of biological and biomedical knowledge bases with over 500 of them and millions of triples. Such knowledge bases are primarily developed for information retrieval, query processing, data integration, standardization, and provision. Developing machine learning methods which can exploit the background knowledge in such resources for predictive analysis and novel discovery in the biomedical domain has become essential. In this dissertation, we present novel approaches which utilize the plethora of data sets made available as bio-ontologies and Linked Data in a single uni ed framework as knowledge graphs. We utilize representation learning with knowledge graphs and introduce generic models for addressing and tackling computational problems of major implications to human health, such as predicting disease-gene associations and drug repurposing. We also show that our methods can compensate for incomplete information in public databases and can smoothly facilitate integration with biomedical literature for similar prediction tasks. Furthermore, we demonstrate that our methods can learn and extract features that outperform relevant methods, which rely on manually crafted features and laborious features engineering and pre-processing. Finally, we present a systematic evaluation of knowledge graph representation learning methods and demonstrate their potential applications for data analytics in biomedicine.