We demonstrate the mitigation of stimulated Brillouin scattering (SBS) in a double-clad single mode Yb-doped optical fiber amplifier through external phase modulation of narrow linewidth laser radiation using optimized periodic waveforms from an arbitrary waveform generator. Such optimized phase modulation waveforms are obtained through a multi-objective Pareto optimization based on a comprehensive model for SBS in high power narrow linewidth fiber amplifiers using Brillouin parameters determined from controlled measurements. The ability of our approach to mitigate SBS is tested experimentally as a function of RMS linewidth of the modulated optical radiation, and we measure an enhancement in SBS threshold with respect to optical linewidth of ∼ 10 GHz-1. Furthermore, we discuss the dependence of the SBS threshold enhancement on key parameters such as the amplifier length and the period of the optimized waveforms. Through simulations we find that waveforms of sufficiently long periods and optimized for a relatively long fiber (10 m) are effective for SBS suppression for shorter fibers as well. We also investigate the effect of increase in the bandwidth and amplitude of the modulation waveform on the SBS threshold enhancement observed at higher optical linewidth.