Cloud radio access network (C-RAN), regarded as a promising green network architecture, facilitates cooperative transmission among remote radio heads (RRHs) while enabling flexible computation provisioning in the virtualized baseband unit pool. By jointly optimizing cooperative transmission, i.e., transmit power allocation with zero-forcing precoding adopted, and computation provisioning, i.e., virtual machine assignment, this paper minimizes the system power consumption comprised of transmit power and processing power in downlink C-RAN. Specifically, subject to per-RRH power constraint (PRPC) and per-MU quality of service constraint, the system power consumption minimization problem is formulated as a mixed integer nonlinear programming (MINLP) problem. To solve the challenging MINLP, we reformulate the MINLP as a minimum weight perfect matching problem to get the initial solution without considering the PRPC. On this basis, a power-aware greedy algorithm is further devised to modify the solution such that the PRPC is satisfied. Finally, extensive simulations show the superiority of the proposed scheme on system power saving and the tradeoff between transmit power and processing power.