Mobile health diagnostics have been shown to be effective and scalable for chronic disease detection and management. By maximizing the smartphones' optics and computational power, they could allow assessment of physiological information from the morphology of pulse waves and thus estimate cuffless blood pressure (BP). We trained the parameters of an existing pulse wave analysis algorithm (oBPM), previously validated in anaesthesia on pulse oximeter signals, by collecting optical signals from 51 patients fingertips via a smartphone while simultaneously acquiring BP measurements through an arterial catheter. We then compared smartphone-based measurements obtained on 50 participants in an ambulatory setting via the OptiBP app against simultaneously acquired auscultatory systolic blood pressure (SBP), diastolic blood pressure (DBP) and mean blood pressure (MBP) measurements. Patients were normotensive (70.0% for SBP versus 61.4% for DBP), hypertensive (17.1% vs. 13.6%) or hypotensive (12.9% vs. 25.0%). The difference in BP (mean ± standard deviation) between both methods were within the ISO 81,060-2:2018 standard for SBP (- 0.7 ± 7.7 mmHg), DBP (- 0.4 ± 4.5 mmHg) and MBP (- 0.6 ± 5.2 mmHg). These results demonstrate that BP can be measured with accuracy at the finger using the OptiBP smartphone app. This may become an important tool to detect hypertension in various settings, for example in low-income countries, where the availability of smartphones is high but access to health care is low.