Optimal transport has emerged as a promising and useful tool for supporting modern image processing applications such as medical imaging and scientific visualization. Indeed, the optimal transport theory enables great flexibility in modeling problems related to image registration, as different optimization resources can be successfully used as well as the choice of suitable matching models to align the images. In this paper, we introduce an automated framework for fundus image registration which unifies optimal transport theory, image processing tools, and graph matching schemes into a functional and concise methodology. Given two ocular fundus images, we construct representative graphs which embed in their structures spatial and topological information from the eye's blood vessels. The graphs produced are then used as input by our optimal transport model in order to establish a correspondence between their sets of nodes. Finally, geometric transformations are performed between the images so as to accomplish the registration task properly. Our formulation relies on the solid mathematical foundation of optimal transport as a constrained optimization problem, being also robust when dealing with outliers created during the matching stage. We demonstrate the accuracy and effectiveness of the present framework throughout a comprehensive set of qualitative and quantitative comparisons against several influential state-of-the-art methods on various fundus image databases.