An electronic device may be provided with a display having a backlight with light sources of different colors. The electronic device may include a color ambient light sensor that measures the color of ambient light and control circuitry that adjusts the color of light emitted from the backlight based on the color of ambient light. The light sources may include at least first and second light-emitting diodes that emit light having different color temperatures. The control circuitry may adjust the intensity of light emitted from the first light-emitting diode relative to the intensity of light emitted from the second light-emitting diode to produce a backlight color that more closely matches the color of ambient light. The first and second light-emitting diodes may include an ultraviolet light-emitting diode die and a blue light-emitting diode die that are mounted in a common semiconductor package.