We consider the problem of joint link scheduling and power control for wireless networks with average transmission power constraints. Due to the high computational complexity of the optimal policies, we extend the class of greedy link scheduling policies to handle average power constraints. We develop a greedy link scheduling and power control scheme GECS, with provable performance guarantees. We show that the performance of our greedy scheduler can be characterized using the Local Pooling Factor (LPF) of a network graph, which has been previously used to characterize the stability of the Greedy Maximal Scheduling (GMS) policy for wireless networks. We also simulate the performance of GECS on wireless network, and compare its performance to another candidate greedy link scheduling and power control policy.