Learning pharmacogenomic multi-relations among diseases, genes and chemicals from content-rich biomedical and biological networks can provide important guidance for drug discovery, drug repositioning and disease treatment. Most of the existing methods focus on imputing missing values in the disease-gene, disease chemical and gene-chemical pairwise relations from the observed relations instead of being designed for learning high-order disease-gene-chemical multi-relations. To achieve the goal, we propose a general tensor-based optimization framework and a scalable Graph-Regularized Tensor Completion from Observed Pairwise Relations (GT-COPR) algorithm to infer the multi-relations among the entities across multiple networks in a low-rank tensor, based on manifold regularization with the graph Laplacian of a Cartesian, tensor or strong product of the networks, and consistencies between the collapsed tensors and the observed bipartite relations. Our theoretical analyses also prove the convergence and efficiency of GT-COPR. In the experiments, the tensor fiber-wise and slice-wise evaluations demonstrate the accuracy of GT-COPR for predicting the diseasegene-chemical associations across the large-scale protein-protein interactions network, chemical structural similarity network and phenotype-based human disease network; and the validation on Genomics of Drug Sensitivity in Cancer cell line dataset shows a potential clinical application of GT-COPR for learning diseasespecific chemical-gene interactions. Statistical enrichment analysis demonstrates that GT-COPR is also capable of producing both topologically and biologically relevant disease, gene and chemical components with high significance.