Positron emission tomography (PET) imaging plays an indispensable role in early disease detection and postoperative patient staging diagnosis. However, PET imaging requires not only additional computed tomography (CT) imaging to provide detailed anatomical information but also attenuation correction (AC) maps calculated from CT images for precise PET quantification, which inevitably demands that patients undergo additional doses of ionizing radiation. To reduce the radiation dose and simultaneously obtain high-quality PET/CT images, in this work, we present an alternative based on deep learning that can estimate synthetic attenuation corrected PET (sAC PET) and synthetic CT (sCT) images from non-attenuation corrected PET (NAC PET) scans for whole-body PET/CT imaging. Our model consists of two stages: the first stage removes noise and artefacts in the NAC PET images to generate sAC PET images, and the second stage synthesizes CT images from the sAC PET images obtained in the first stage. Both stages employ the same deep Wasserstein generative adversarial network and identical loss functions, which encourage the proposed model to generate more realistic and satisfying output images. To evaluate the performance of the proposed algorithm, we conducted a comprehensive study on a total of 45 sets of paired PET/CT images of clinical patients. The final experimental results demonstrated that both the generated sAC PET and sCT images showed great similarity to true AC PET and true CT images based on both qualitative and quantitative analyses. These results also indicate that in the future, our proposed algorithm has tremendous potential for reducing the need for additional anatomic imaging in hybrid PET/CT systems or the need for lengthy MR sequence acquisition in hybrid PET/MRI systems.