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Culverts fulfill the vital function of safely channeling water beneath railway tracks, highways, and overpasses. They serve various purposes, including facilitating drainage in areas such as watercourses, drainage zones, and regions with restricted ground-bearing capacity. Precast reinforced concrete (RC) box culverts are a popular choice because they are strong, durable, rigid, and economical. However, culverts are prone to corrosion due to exposure to a range of environmental factors and aggressive chemicals. Therefore, enhancing the design and construction of this crucial infrastructure is imperative to effectively combat corrosion and to adhere to modern standards of reliability and affordability. In this study, carbon fiber-reinforced polymer (CFRP) was used to strengthen corroded culverts, with promising potential to improve safety and longevity in these structures. This study compared the behavior of corroded RC box culverts to CFRP-strengthened ones using the finite element method (FEM). It explored the impact of varying the damage thicknesses owing to corrosion, ranging from 0 mm to 20 mm, on the structural performance of the box culverts. The results showed that the CFRP model exhibited a substantial 25% increase in the capacity and reduced the damage compared to the reference model. Moreover, a parametric study was conducted for establishing a cost-effective design, in which numerous CFRP strip configurations were examined for a damaged-culvert model. The results indicated that a complete CFRP sheet was most effective for the maximum design capacity and repair effectiveness. The study’s outcomes provide valuable insights for professionals engaged in enhancing the strength of box culverts, aiming to increase the capacity, enhance the stability, and strengthen corroded culverts.