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For diagnosis of COVID-19, a SARS-CoV-2 virus-specific reverse transcriptase polymerase chain reaction (RT-PCR) test is routinely used. However, this test can take up to two days to complete, serial testing may be required to rule out the possibility of false negative results, and there is currently a shortage of RT-PCR test kits, underscoring the urgent need for alternative methods for rapid and accurate diagnosis of COVID-19 patients. Chest computed tomography (CT) is a valuable component in the evaluation of patients with suspected SARS-CoV-2 infection. Nevertheless, CT alone may have limited negative predictive value for ruling out SARS-CoV-2 infection, as some patients may have normal radiologic findings at early stages of the disease. In this study, we used artificial intelligence (AI) algorithms to integrate chest CT findings with clinical symptoms, exposure history, and laboratory testing to rapidly diagnose COVID-19 positive patients. Among a total of 905 patients tested by real-time RT-PCR assay and next-generation sequencing RT-PCR, 419 (46.3%) tested positive for SARS-CoV-2. In a test set of 279 patients, the AI system achieved an AUC of 0.92 and had equal sensitivity as compared to a senior thoracic radiologist. The AI system also improved the detection of RT-PCR positive COVID-19 patients who presented with normal CT scans, correctly identifying 17 of 25 (68%) patients, whereas radiologists classified all of these patients as COVID-19 negative. When CT scans and associated clinical history are available, the proposed AI system can help to rapidly diagnose COVID-19 patients.