Recently, Cloud-based Radio Access Network (C-RAN) has been proposed as a potential solution to reduce energy cost in cellular networks. C-RAN centralizes the baseband processing capabilities of Base Stations (BSs) in a cloud computing platform in the form of BaseBand Unit (BBU) pool. In C-RAN, power consumed by the traditional BS system is distributed as wireless transmission power of the Remote Radio Heads (RRHs) and baseband processing power of the BBU pool. Different from previous work where wireless transmission power and baseband processing power are optimized individually and independently, this paper focuses on joint optimization of allocation for these two kinds of power and attempts to minimize the total power consumption subject to Quality of Service (QoS) requirements from users in terms of data rates. First, we exploit the load coupling model to express the coupling relations among power, load and user data rates. Based on the load coupling mode, we formulate the joint power optimization problem in C-RAN over both wireless transmission power and baseband processing power. Second, we prove that operating at full load may not be optimal in minimizing the total power consumption in C-RAN. Finally, we propose an efficient iterative algorithm to solve the target problem. Simulations have been performed to validate our theoretical and algorithmic work. The results show that the proposed algorithm outperforms existing schemes (without joint power optimization) in terms of power consumption.