Active control of the amplitude and frequency of terahertz sources is an essential prerequisite for exploiting a myriad of terahertz applications in imaging, spectroscopy, and communications. Here we present an optoelectronic, external modulation technique applied to a terahertz quantum cascade laser which holds the promise of addressing a number of important challenges in this research area. A hybrid metamaterial/graphene device is implemented into an external cavity set-up allowing for optoelectronic tuning of feedback into a quantum cascade laser. We demonstrate powerful, all-electronic, control over the amplitude and frequency of the laser output. Full laser switching is performed by electrostatic gating of the metamaterial/graphene device, demonstrating a modulation depth of 100 %. External control of the emission spectrum is also achieved, highlighting the flexibility of this feedback method. By taking advantage of the frequency dispersive reflectivity of the metamaterial array, different modes of the QCL output are selectively suppressed using lithographic tuning and single mode operation of the multi-mode laser is enforced. Side mode suppression is electrically modulated from ~6 dB to ~21 dB, demonstrating active, optoelectronic modulation of the laser frequency content between multi-mode and single mode operation.