Studying viral-host protein-protein interactions can facilitate the discovery of therapies for viral infection. We use high-throughput yeast two-hybrid experiments and mass spectrometry to generate a comprehensive SARS-CoV-2-human protein-protein interactome network consisting of 739 high-confidence binary and co-complex interactions, validating 218 known SARS-CoV-2 host factors and revealing 361 novel ones. Our results show the highest overlap of interaction partners between published datasets and of genes differentially expressed in samples from COVID-19 patients. We identify an interaction between the viral protein ORF3a and the human transcription factor ZNF579, illustrating a direct viral impact on host transcription. We perform network-based screens of >2,900 FDA-approved or investigational drugs and identify 23 with significant network proximity to SARS-CoV-2 host factors. One of these drugs, carvedilol, shows clinical benefits for COVID-19 patients in an electronic health records analysis and antiviral properties in a human lung cell line infected with SARS-CoV-2. Our study demonstrates the value of network systems biology to understand human-virus interactions and provides hits for further research on COVID-19 therapeutics.