We present a rapid-scanning approach to fluorescence-detected two-dimensional electronic spectroscopy that combines acousto-optic phase-modulation with digital lock-in detection. This approach shifts the signal detection window to suppress 1/f laser noise and enables interferometric tracking of the time delays to allow for correction of spectral phase distortions and accurate phasing of the data. This use of digital lock-in detection enables acquisition of linear and nonlinear signals of interest in a single measurement. We demonstrate the method on a laser dye, measuring the linear fluorescence excitation spectrum as well as rephasing, non-rephasing, and absorptive fluorescence-detected two-dimensional electronic spectra.