Conditional Random Fields (CRFs) are often used to improve the output of an initial segmentation model, such as a convolutional neural network (CNN). Conventional CRF approaches in medical imaging use manually defined features, such as intensity to improve appearance similarity or location to improve spatial coherence. These features work well for some tasks, but can fail for others. For example, in medical image segmentation applications where different anatomical structures can have similar intensity values, an intensity-based CRF may produce incorrect results. As an alternative, we propose Posterior-CRF, an end-to-end segmentation method that uses CNN-learned features in a CRF and optimizes the CRF and CNN parameters concurrently. We validate our method on three medical image segmentation tasks: aorta and pulmonary artery segmentation in non-contrast CT, white matter hyperintensities segmentation in multi-modal MRI, and ischemic stroke lesion segmentation in multi-modal MRI. We compare this with the state-of-the-art CNN-CRF methods. In all applications, our proposed method outperforms the existing methods in terms of Dice coefficient, average volume difference, and lesion-wise F1 score.