Clock synchronization is critical for maintaining low error rates in quantum key distribution. Here, we describe how a frequency mismatch between the transmitter and receiver clocks affects the quantum bit error rate in quantum key distribution, and derive from this model a simple synchronization algorithm together with clock stability requirements for practical operation. Our algorithm continuously compensates for both frequency mismatch and time-offset fluctuations directly from detection timestamps, whereas absolute time-offset determination, performed separately from the algorithm, is achieved once using conventional cross-correlation with a known qubit sequence. The algorithm has linear time complexity overall, while its per-iteration computational cost, once histograms have been formed, is independent of the frequency-mismatch range and accuracy. The algorithm does not require a dedicated synchronization channel or auxiliary qubit sequence, it converges from a large frequency mismatch within approximately one second of photon acquisition, and remains effective in low-photon-count regimes (more than 30 dB of channel loss) using standard hardware. Finally, we validate our approach by demonstrating successful key exchange over 100 km of fiber and continuous operation over 24 hours in a 16 km metropolitan network using commercial systems, with performance equivalent to using a service channel for clock synchronization.