Unsupervised deep-learning (DL) models were recently proposed for deformable image registration tasks. In such models, a neural-network is trained to predict the best deformation field by minimizing some dissimilarity function between the moving and the target images. We introduce a fully Bayesian framework for unsupervised DL-based deformable image registration. Our method provides a principled way to characterize the true posterior distribution, thus, avoiding potential over-fitting. We demonstrated the added-value of our Bayesian unsupervised DL-based registration framework on the MNIST and brain MRI (MGH10) datasets in comparison to the VoxelMorph. Our experiments show that our approach provided better estimates of the deformation field by means of improved mean-squared-error (0.0063 vs. 0.0065) and Dice coefficient (0.73 vs. 0.71) for the MNIST and the MGH10 datasets, respectively. Further, it provides an estimate of the uncertainty in the deformation-field.