Using fiber-reinforced polymer (FRP) wraps has proven to be an effective and optimized confinement technique to upgrade the axial and flexural capacity of reinforced concrete (RC) and reinforced masonry (RM) columns. The axial capacity of FRP-confined masonry depends on both the compressive strength of masonry before strengthening and the confinement pressure provided by the FRP jacket. This study proposes a simplified methodology to design and analyze prismatic fully grouted reinforced masonry columns (RMCs) strengthened with FRP Jackets. The proposed design methodology included an analytical confinement model to predict the compressive strength gain in RMCs due to the effective confinement pressure provided by FRP jackets. The proposed procedure was also designed to predict the nominal capacity of RMCs for practical design applications, with columns subjected to both axial loading and bending moment. The essential parameters to perform detailed section analysis were established, and suggested expressions were proposed to obtain the parameter values. Practical values for the equivalent rectangular stress block parameters were proposed. The theoretical axial force-moment interaction diagrams obtained by the proposed procedure were compared with available experimental data. The experimental test results were in good agreement with the analytical predictions by a reasonable marginal error. Furthermore, the effect of five design variables on the axial-flexural interaction of FRP-wrapped RMCs was investigated. The variables considered in the parametric study were the number of FRP layers, radius of the corners, stiffness of the FRP composite, cross-sectional aspect ratio, and masonry compressive strength. The results showed that increasing the FRP layers, corner radius, and FRP jacket stiffness significantly enhanced the axial capacity of the FRP-confined RMCs. However, the increase in the masonry compressive strength and cross-sectional aspect ratio negatively affected the axial capacity gain ratio of FRP-strengthened RMCs.