This study presents a novel optimization-based framework for the design of offshore wind power farms (OWFs). In the framework, the characteristics of the OWF facilities are decided. Then, feasible locations for installing the facilities are identified by utilizing geographical information system (GIS). Finally, a MIFP optimization model is formulated for micro-siting of turbines and offshore substations, cable routes, and grid connection, by minimizing levelized cost of electricity. A case study is performed in Jeju Island, South Korea. The unit capital cost of the resulting optimal OWF design in Jeju Island is estimated as 2.3 MM$/MW, which is at par with existing and planned OWFs. Scenario analyses are performed to examine the effect of the spatiotemporal resolution of the model on the optimized design and cost of the wind farm. Moreover, a stochastic programming formulation is proposed to address the wind uncertainties and the resulting design shows improved or equal economics.