Energy efficiency has emerged as a key concern for modern processor design, especially when it comes to embedded and mobile devices. It is vital to accurately quantify the power consumption of different micro-architectural components in a CPU. Traditional RTL or gate-level power estimation is too slow for early design-space exploration studies. By contrast, existing architecture-level power models suffer from large inaccuracies. Recently, advanced machine learning techniques have been proposed for accurate power modeling. However, existing approaches still require slow RTL simulations, have large training overheads or have only been demonstrated for fixed-function accelerators and simple in-order cores with predictable behavior. In this work, we present a novel machine learning-based approach for microarchitecture-level power modeling of complex CPUs. Our approach requires only high-level activity traces obtained from microarchitecture simulations. We extract representative features and develop low-complexity learning formulations for different types of CPU-internal structures. Cycle-accurate models at the sub-component level are trained from a small number of gate-level simulations and hierarchically composed to build power models for complete CPUs. We apply our approach to both in-order and out-of-order RISC-V cores. Cross-validation results show that our models predict cycle-by-cycle power consumption to within 3% of a gate-level power estimation on average. In addition, our power model for the Berkeley Out-of-Order (BOOM) core trained on micro-benchmarks can predict the cycle-by-cycle power of real-world applications with less than 3.6% mean absolute error.