Genetically encoded fluorescent reporters of membrane potential promise to reveal aspects of neural function not detectable by other means. We present a palette of multicoloured brightly fluorescent genetically encoded voltage indicators with sensitivities from 8-13% ΔF/F per 100 mV, and half-maximal response times from 4-7 ms. A fluorescent protein is fused to an archaerhodopsin-derived voltage sensor. Voltage-induced shifts in the absorption spectrum of the rhodopsin lead to voltage-dependent nonradiative quenching of the appended fluorescent protein. Through a library screen, we identify linkers and fluorescent protein combinations that report neuronal action potentials in cultured rat hippocampal neurons with a single-trial signal-to-noise ratio from 7 to 9 in a 1 kHz imaging bandwidth at modest illumination intensity. The freedom to choose a voltage indicator from an array of colours facilitates multicolour voltage imaging, as well as combination with other optical reporters and optogenetic actuators.