Abstract: The cosmological constant problem represents a 120-order-of-magnitude discrepancy between Quantum Field Theory predictions and observations. In this work, we provide a first-principles derivation of the Holographic Dark Energy (HDE) density based on Horizon Thermodynamics. Key Results: Thermodynamic Origin: We demonstrate that Dark Energy arises as the thermodynamic cost required to process information on the expanding cosmic horizon ($dE = T_h dS$). Resolution of the Hierarchy Problem: We derive the correct order of magnitude for the vacuum energy ($\rho \sim 10^{-27}$ kg/m³) without fine-tuning. The Renormalization Factor: We identify a universal holographic efficiency factor, $\xi \approx 1/3$, which emerges independently from two constraints: dynamic consistency with Friedmann equations and agreement with observational data. Context: This work constitutes the geometric foundation of the Cosmology of Time framework. It complements previous derivations linking Dark Energy to information processing costs and Dark Matter to information storage capacity.