Advancements in metal Additive Manufacturing (AM) have enabled the production of lightweight and functional metallic parts. In particular, Wire and Arc Additive Manufacturing (WAAM) processes have gained prominence due to their efficiency and high deposition rates. However, the WAAM process generates residual stresses (RS), wherein the tensile RS may degrade the base metal’s mechanical properties but can enhance the load-bearing capacity by essentially prestressing specific parts (i.e., the flange tips) of steel sections against subsequent applied compressive loading. Therefore, it is crucial to design a WAAM stiffener so that the structure benefits not only from the imposed geometry, but also from the induced RS. While previous research has identified heat source and material type as influencing factors on RS, there is little consideration of critical parameters such as deposition layer (stiffener) position, layer count, and base plate thickness. This paper provides insight into the impact of such design parameters on the resulting RS from WAAM deposition of a stiffener on a base plate through validated finite element (FE) modelling. The base plate is simulated for both clamped and unclamped conditions. The results demonstrate that adding WAAM stiffeners on the webs of I-sections generates tensile RS in their vicinity, with peak values reaching the material’s yield strength. Moreover, increasing the base plate or stiffener thickness reduces the RS relative to the mid-thickness of each base plate. While the location of the stiffener does not significantly affect the magnitude of the peak RS, it causes a shift in the RS pattern and distribution. The results presented in this paper can be used to infer appropriate WAAM design parameters to achieve favorable RS patterns, enhancing the quality of manufactured parts for new production or the repair and reinforcement of existing infrastructure.