Obstructive sleep apnea (OSA) affects more than 900 million adults globally and can create serious health complications when untreated; however, 80% of cases remain undiagnosed. Critically, current diagnostic techniques are fundamentally limited by low throughputs and high failure rates. Here, we report a wireless, fully integrated, soft patch with skin-like mechanics optimized through analytical and computational studies to capture seismocardiograms, electrocardiograms, and photoplethysmograms from the sternum, allowing clinicians to investigate the cardiovascular response to OSA during home sleep tests. In preliminary trials with symptomatic and control subjects, the soft device demonstrated excellent ability to detect blood-oxygen saturation, respiratory effort, respiration rate, heart rate, cardiac pre-ejection period and ejection timing, aortic opening mechanics, heart rate variability, and sleep staging. Last, machine learning is used to autodetect apneas and hypopneas with 100% sensitivity and 95% precision in preliminary at-home trials with symptomatic patients, compared to data scored by professionally certified sleep clinicians.