Patients with coronavirus disease 2019 (COVID-19) present with a range of devastating acute clinical manifestations affecting the lungs, liver, kidneys and gut. The best-characterized entry receptor for the disease-causing virus SARS-CoV2, angiotensin converting enzyme (ACE) 2, is highly expressed in these tissues. However, the pathways that underlie the disease are still poorly understood. Here we show that the complement system is unexpectedly one of the intracellular pathways most highly induced by SARS-CoV2 infection in lung epithelial and liver cells. Within cells of the bronchoalveolar lavage of patients, distinct signatures of complement activation in myeloid, lymphoid and epithelial cells tracked with disease severity. Modelling the regulome of host genes induced by COVID-19 and the drugs that could normalize these genes both implicated the JAK1/2-STAT1 signaling system downstream of type I interferon receptors, and NF-kB. Ruxolitinib, a JAK1/2 inhibitor and the top predicted pharmaceutical candidate, normalized interferon signature genes, IL-6 (the best characterized severity marker in COVID-19) and all complement genes induced by SARS-CoV2, but did not affect NF-kB-regulated genes. We predict that combination therapy with JAK inhibitors and other agents with the potential to normalize NF-kB-signaling, such as anti-viral agents, may serve as an effective clinical strategy.