We present a novel FPGA-based bismuth germanate (BGO) time-of-flight (TOF) digitizer, implemented on an FPGA (XC7VX485T-2FFG1761C, Xilinx). This digitizer is designed to address the recently highlighted characteristics of BGO, which generates both scintillation and prompt Cerenkov photons when a 511-keV photon interacts with BGO. The developed digitizer independently processes these two types of photons for precise energy and timing measurements. The digitizer incorporates a noise-resistant binary counter that measures energy signals using the time-over-threshold (TOT) method. For timing measurements, we employ an embedded dual-side monitoring time-to-digital converter, which efficiently captures timing information while maintaining low resource usage. We validated the efficacy of our FPGA-based TOF digitizer through extensive experiments, including both electrical testing and coincidence measurements using BGO pixels. Our evaluations of TOT energy and timing performance utilized two 3 × 3 × 20 mm