Background: Continuous vital sign monitoring using wearable sensors has gained traction for the early detection of patient deterioration, particularly with the advent of virtual wards. Objective: The objective was to evaluate the reliability of a wearable sensor for monitoring heart rate (HR), respiratory rate (RR), and temperature in acutely unwell hospital patients and to identify the optimal time window for alert generation. Methods: A prospective cohort study recruited 500 patients in a single hospital. Sensor readings were compared to standard intermittent nurse observations using Bland–Altman plots to assess the limits of agreement. Results: HR demonstrated good agreement with nurse observations (intraclass correlation coefficient [ICC] = 0.66, r = 0.86, p < 0.001), with a mean difference of 3.63 bpm (95% LoA: −10.87 to 18.14 bpm). RR exhibited weaker agreement (ICC = 0.20, r = 0.18, p < 0.001), with a mean difference of −2.72 breaths per minute (95% LoA: −10.91 to 5.47 bpm). Temperature showed poor to fair agreement (ICC = 0.30, r = 0.39, p < 0.001), with a mean difference of −0.57 °C (95% LoA: −1.72 to 0.58 °C). A 10 min averaging window was identified as optimal, balancing data retention and real-time alerting. Conclusions: Wearable sensors demonstrate potential for reliable continuous monitoring of vital signs, supporting their future integration into real-world clinical practice for improved patient safety.