Elastic fibers provide critical elasticity to the arteries, lungs, and other organs. Elastic fiber assembly is a process where soluble tropoelastin is coacervated into liquid droplets, cross-linked, and deposited onto and into microfibrils. While much progress has been made in understanding the biology of this process, questions remain regarding the timing of interactions during assembly. Furthermore, it is unclear to what extent fibrous templates are needed to guide coacervate droplets into the correct architecture. The organization and shaping of coacervate droplets onto a fiber template have never been previously modeled or employed as a strategy for shaping elastin fiber materials. Using an in vitro system consisting of elastin-like polypeptides (ELPs), genipin cross-linker, electrospun polylactic-co-glycolic acid (PLGA) fibers, and tannic acid surface coatings for fibers, we explored ELP coacervation, cross-linking, and deposition onto fiber templates. We demonstrate that integration of coacervate droplets into a fibrous template is primarily influenced by two factors: (1) the balance of coacervation and cross-linking and (2) the surface energy of the fiber templates. The success of this integration affects the mechanical properties of the final fiber network. Our resulting membrane materials exhibit highly tunable morphologies and a range of elastic moduli (0.8-1.6 MPa) comparable to native elastic fibers.