In this study, a performance evaluation was conducted on a composite elastic asphalt precast expansion joint developed to replace steel expansion joints that frequently suffer from various damages, such as blow-up owing to increased traffic volume and abnormal weather. Two types of elastic asphalt binders were prepared by mixing a latex-based modifier, and their basic properties and performance were evaluated. Elastic asphalt binders were mixed with 8–13 and 13–19 mm aggregates to prepare elastic asphalt joint mixtures, and their permanent deformation and adhesive performance were evaluated using Hamburg wheel-tracking and direct-shear tests. Elastic asphalt joint blocks and internal reinforcement for crack prevention were applied to produce the elastic composite expansion joints, and their performance was evaluated through contraction–extension tests to determine fatigue cracking, maximum load during contraction– extension, and repeated contraction–extension tests. As a result of the performance evaluation of the developed elastic asphalt binder, both the high- and low-temperature performances were improved, and the temperature sensitivity was superior to that of general asphalt binders, exhibiting high resistance to cracking. In addition, the joint block specimens manufactured by mixing the elastic asphalt binder with 13–19 mm aggregates exhibited excellent permanent deformation in the dynamic stability and Hamburg wheel-tracking tests, and they had higher adhesive performance than the method of repairing with rapid-hardening concrete materials at low and room temperatures, where significant contraction of the concrete joint occurs. We confirmed that when a compression spring-type reinforcement was applied, the compressive force for contraction decreased significantly compared with the unreinforced state, and the tensile force for extension increased, thereby reducing the stress applied to the mixture itself. The composite elastic asphalt precast expansion joint developed in this study is expected to have superior durability against cracks and secure continuity with the road surface through the tensile force dispersing effect using expansion reinforcement. Thus, it has better drivability than the existing steel expansion joint and can absorb shocks such as vibrations and noise applied to a structure.