This study provides an overview of the production costs of methane and hydrogen via water electrolysis-based hydrogen production followed by a methanation based methane production technology utilizing CO2 from external sources. The study shows a comparative way for economic optimization of green methane generation using excess free electricity from renewable sources. The study initially developed the overall process on the Aspen Plus simulation tool. Aspen Plus estimated the capital expenditure for most of the equipment except for the methanation reactor and electrolyzer. The capital expenditure, the operating expenditure and the feed cost were used in a discounted cash flow based economic model for the methane production cost estimation. The study compared different reactor configurations as well. The same model was also used for a hydrogen production cost estimation. The optimized economic model estimated a methane production cost of $11.22/mcf when the plant is operating for 4000 hr/year and electricity is available for zero cost. Furthermore, a hydrogen production cost of $2.45/GJ was obtained. A sensitivity analysis was performed for the methane production cost as the electrolyzer cost varies across different electrolyzer types. A sensitivity study was also performed for the changing electricity cost, the number of operation hours per year and the plant capacity. The estimated levelized cost of methane (LCOM) in this study was less than or comparable with the existing studies available in the literature.