Fluorescence resonance energy transfer (FRET) is a promising means of enabling information processing in nanoscale devices, but dynamic control over exciton pathways is required. Here, we demonstrate the operation of two complementary switches consisting of diffusive FRET transmission lines in which exciton flow is controlled by DNA. Repeatable switching is accomplished by the removal or addition of fluorophores through toehold-mediated strand invasion. In principle, these switches can be networked to implement any Boolean function.