The invention provides a body-worn system that continuously measures pulse oximetry and blood pressure, along with motion, posture, and activity level, from an ambulatory patient. The system features an oximetry probe that comfortably clips to the base of the patient's thumb, thereby freeing up their fingers for conventional activities in a hospital, such as reading and eating. The probe secures to the thumb and measures time-dependent signals corresponding to LEDs operating near 660 and 905 nm. Analog versions of these signals pass through a low-profile cable to a wrist-worn transceiver that encloses a processing unit. Also within the wrist-worn transceiver is an accelerometer, a wireless system that sends information through a network to a remote receiver, e.g. a computer located in a central nursing station.