In the past 20 years, there have been several infectious disease outbreaks in humans for which the causative agent has been a zoonotic coronavirus. Novel infectious disease outbreaks, as illustrated by the current coronavirus disease 2019 (COVID-19) pandemic, demand a rapid response in terms of identifying effective treatments for seriously ill patients. The repurposing of approved drugs from other therapeutic areas is one of the most practical routes through which to approach this. Here, we present a systematic network-based drug repurposing methodology, which interrogates virus-human, human protein-protein and drug-protein interactome data. We identified 196 approved drugs that are appropriate for repurposing against COVID-19 and 102 approved drugs against a related coronavirus, severe acute respiratory syndrome (SARS-CoV). We constructed a protein-protein interaction (PPI) network based on disease signatures from COVID-19 and SARS multi-omics datasets. Analysis of this PPI network uncovered key pathways. Of the 196 drugs predicted to target COVID-19 related pathways, 44 (hypergeometric p-value: 1.98e-04) are already in COVID-19 clinical trials, demonstrating the validity of our approach. Using an artificial neural network, we provide information on the mechanism of action and therapeutic value for each of the identified drugs, to facilitate their rapid repurposing into clinical trials.