Geo-encased stone columns (GESCs), known for their cost-effectiveness and simple construction, are widely employed in the reinforcement of soft soil foundations in practical engineering, and the analysis of their settlement serves as a crucial foundation for the design process. However, existing research mainly focuses on experimental and numerical methods, with relatively limited progress in theoretical calculations. Based on the load transfer mechanism of GESC-reinforced composite foundations and the bulging deformation of the pile body within a certain depth of the pile top under vertical loading, the reinforced zone was divided into a bulging section and a non-bulging section, and the total settlement of the pile was regarded as the sum of the compression in these two sections. A settlement calculation formula for the GESC-reinforced composite foundation was derived with consideration of the deformation compatibility between the pile, the geosynthetic encasement, and the soil. To verify the feasibility of the proposed method, a practical engineering case was analyzed using the formula. On this basis, parameter analysis was conducted. The results show that the load–settlement curve obtained from the theoretical calculation closely matches that from the field test, confirming the feasibility of the proposed method. The settlement of the GESC-reinforced composite foundation decreases with the increase in encasement strength, encasement depth, soil cohesion around the pile, and area replacement ratio, but it increases with the increase in pile-soil stress ratio. Moreover, there exists an optimal encasement depth; when the encasement depth exceeds the optimal value, increasing the encasement length has little effect on reducing the settlement of the composite foundation.