This paper investigates optimal relay selection and power allocation under an aggregate power constraint for cooperative wireless sensor networks assisted by amplify-and-forward relay nodes. By considering both transmission power and circuit power consumptions, the received signal-to-noise ratio (SNR) at the destination node is calculated, based on which, a relay selection and power allocation scheme is developed. The core idea is to adaptively adjust the selected relays and their transmission power to maximize the received SNR according to the channel state information. The proposed scheme is derived by recasting the optimization problem into a three-layered problem-determining the number of relays to be activated, selecting the active relays, and performing power allocation among the selected relays. Monte Carlo simulation results demonstrate that the proposed scheme provides a higher received SNR and a lower bit error rate as compared to the average power allocation scheme.