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Abstract: This paper develops a comprehensive stochastic control framework for optimal execution that systematically incorporates self-exciting order flow dynamics through Hawkes processes. While classical execution models like Almgren-Chriss and Obizhaeva-Wang provide foundational insights, they fail to capture the clustered order flow patterns empirically observed in modern electronic markets. Our framework bridges this gap by embedding multivariate Hawkes processes within a transient price impact model, yielding adaptive execution strategies that respond intelligently to market microstructure conditions. Theoretical contributions include the derivation of closed-form optimal policies under exponential kernel specifications, the establishment of rigorous viability conditions that prevent price manipulation, and the development of a Markovian representation that maintains tractability while approximating power-law decay patterns through complete monotone mixtures. The resulting Hawkes-LQ controller decomposes optimally into baseline, trend-following, and dynamic components, providing both mathematical rigor and economic intuition. Empirical analysis demonstrates economically significant and statistically robust improvements over classical benchmarks. Across extensive Monte Carlo simulations and empirical validation on equity data, the Hawkes-LQ strategy achieves cost reductions of 7.8%-15.8% versus industry standards, with particularly strong performance in the medium-to-high clustering regimes empirically observed across major stocks. Beyond cost reduction, the framework provides superior risk management characteristics, including 14.6% lower Value-at-Risk and more predictable execution outcomes. The framework maintains practical implementability with computational requirements suitable for real-time deployment and demonstrates remarkable robustness to model misspecification. Our work provides both a theoretical foundation and practical methodology for the next generation of execution algorithms, addressing the critical need for strategies that adapt to the self-exciting nature of modern financial markets.