With the end of Dennard scaling, energy efficiency has become an important metric driving future processor architectures, particularly in the fields of mobile and embedded devices. To support rapid, power-aware design space exploration, it is important to accurately quantify the power consumption of the different micro-architectural components of processors early in the design flow and at a high level of abstraction. Existing CPU power models rely on either generic analytical power models or simple regression-based techniques that suffer from large inaccuracies. Recently proposed machine learning techniques for accurate power modeling still require slow RTL simulations or have only been demonstrated for fixed-function accelerators at higher levels. In this thesis, we present a novel approach that uses machine-learning to model cycle-accurate power consumption of programmable processors and their internal structures at a high micro-architectural level. Using only high-level information that can be obtained from micro-architecture simulations, we extract representative features and develop low-complexity learning formulations for different micro-architecture components that require a small number of gate-level simulations for training. We further present a hierarchical power model composition methodology to build power models for complete CPUs. Our composed models provide cycle-accurate and hierarchical power estimates down to sub-block granularity. We demonstrate the generality of our approach by modeling a simple in-order core as well as a complex superscalar out-of-order core. Results show that our hierarchically composed models for two RISC-V processor cores, RI5CY core from the PULP platform and Berkeley Out-of-Order Machine (BOOM), predicts cycle-by-cycle power consumption to within 2.2% and within 2.9% of a gate-level power estimation on average, respectively. In addition, our power model for the BOOM core, trained on micro-benchmarks, has an error rate of less than 3.6% when predicting cycle-by-cycle power consumption of a real-world application