An electronic device may be provided with an ambient light sensor. An analog-to-digital converter may be used to digitize ambient light measurements made with the ambient light sensor. Control circuitry in the electronic device may be used to adjust the brightness of a display and take other actions in the electronic device based on the digitized ambient light measurements. The analog-to-digital converter may be a hybrid analog-to-digital converter having a most-significant-bit analog-to-digital converter circuit branch based on an integrating analog-to-digital converter and a least-significant-bit analog-to-digital converter circuit branch based on a successive-approximation-register analog-to-digital converter. The most-significant-bit branch may produce an output based a reset count for an integrator that is reset a number of times during a measurement period. The least-significant-bit branch may produce an output by digitizing an output from the integrator upon termination of the measurement period.