We report on the analysis and prototype characterization of a dual-electrode electro-optic modulator that can generate both amplitude and phase modulations with a selectable relative phase, termed a quadrature variable modulator (QVM). All modulation states can be reached by tuning only the electrical inputs, facilitating real-time tuning, and the device has shown good suppression and stability properties. A mathematical analysis is presented, including the development of a geometric-phase representation for modulation. The experimental characterization of the device shows that relative suppressions of 38, 39, and 30 dB for phase, single sideband, and carrier-suppressed modulations, respectively, can be obtained as well as that the device is well behaved when scanning continuously through the parameter space of modulations. The QVM is compared with existing optical configurations that can produce amplitude and phase-modulation combinations in the context of applications such as the tuning of lock points in optical-locking schemes, single-sideband applications, modulation fast-switching applications, and applications requiring combined modulations.