This paper presents the development and validation of an optimal design methodology for vertical U-tube ground heat exchangers (GHEs) used in HVAC systems. The dimensionless entropy generation number obtained by scaling the entropy generation due to heat transfer and pressure drop, on the ratio of the heat transfer rate to the average fluid temperature of vertical GHEs is employed as the objective function. Five design variables are first selected based on the global sensitivity analysis and then optimized by a genetic algorithm optimization technique. The entropy generation process combines the heat transfer and fluid mechanics with thermodynamic analysis. A case study shows that this optimal design approach can decrease the total system cost (i.e. the upfront cost and 10-year operation cost) by 5.5%, compared with the original design. The entropy generation number (EGN) of the optimal design case is 12.2% less than that of the base design case. From the thermo-economic aspect, decreasing the upfront cost is more important than decreasing the operational cost for the case studied. The results also demonstrate the effectiveness and feasibility of using the entropy generation minimization method for optimal design of vertical GHEs.