Full and arbitrary control of polarization states of light using two independent electro-optic modulators is presented. The mechanism of the controllability is theoretically described using the Jones vector and matrix, and the polarization state change with control parameters is geometrically illustrated in the Stokes parameter space. Our theoretical framework involves possible distortions of the polarization state due to optical elements between the polarization controller and measurement point and presents a mechanism for pre-compensating the polarization distortion. The theory's validity and controllability of the polarization state are experimentally demonstrated with a test optical setup using a dichroic mirror as a polarization distorter. The inevitable intensity variation during polarization sweeps and a strategy for pre- and post-compensation of the variations are discussed. The technique's applicability to bioimaging is also discussed.