A method of assembling a floating wind turbine platform includes assembling a keystone having a hollow central cavity from pre-formed concrete sections, and assembling a plurality of buoyant bottom beams from pre-formed concrete sections. Each bottom beam is attached to, and extends radially outward of the keystone to define a base assembly. Each buoyant bottom beam includes a ballast chamber therein. The keystone is post-tensioned to each bottom beam along a longitudinal axis thereof. A center column is assembled upwardly and perpendicularly on the base assembly from pre-formed sections of the center column, the outer columns are assembled on a distal end of each bottom beam from pre-formed sections of the outer columns, and the center column and the outer columns are longitudinally post-tensioned to the base assembly. A tower is assembled on the center column from pre-formed sections, and a wind turbine is assembled on the tower.