The ability to control the morphologies of biomolecular aggregates is a central objective in the study of self-assembly processes. The development of predictive models offers the surest route for gaining such control. Under the right conditions, proteins will self-assemble into fibers that may rearrange themselves even further to form diverse structures, including the formation of closed loops. In this study, chicken egg white ovalbumin is used as a model for the study of fibril loops. By monitoring the kinetics of self-assembly, we demonstrate that loop formation is a consequence of end-to-end association between protein fibrils. A model of fibril formation kinetics, including end-joining, is developed and solved, showing that end-joining has a distinct effect on the growth of fibrillar mass density (which can be measured experimentally), establishing a link between self-assembly kinetics and the underlying growth mechanism. These results will enable experimentalists to infer fibrillar morphologies from an appropriate analysis of self-assembly kinetic data.