Bihemispheric non-invasive motor cortex stimulation has shown promise for facilitating motor learning and recovery after stroke. However, previous studies yielded mixed results that can primarily be attributed to inter-individual variability in response. We therefore aimed at investigating neural correlates of bihemispheric transcranial direct current stimulation (tDCS) effects using multimodal magnetic resonance imaging (MRI). Twenty-four young healthy adults underwent diffusion tensor imaging (DTI), resting state and task-related functional MRI in a randomized sham-controlled, double-blind study using a triple cross-over design. We compared two active stimulation conditions—bihemispheric (or “dual”) and unihemispheric anodal tDCS—with sham tDCS. The anode was placed over the left primary motor cortex in all conditions, and subgroups of responders were defined according to task-related activity in this area while subjects pressed a response button with their right index fingers during a choice reaction time task. Compared to sham, “dual responders” and “anodal responders” were characterized by mean beta value increases of 86 ± 55% and 126 ± 55%, respectively. In line with electrophysiological studies, tDCS effects on motor cortex activation appeared to be highly variable across the group. At rest, dual tDCS caused widespread bihemispheric alterations of functional connectivity, possibly mediating its most striking effect, which consisted of bilateral motor cortex disinhibition during the task-related functional MRI. In contrast, unihemispheric anodal tDCS was characterized by more local modulations of functional motor networks. As in aging and after stroke, the impact of dual tDCS on the motor system in young adults seems to depend on the microstructural status of transcallosal motor tracts as well. In sum, these results shed light on the neural correlates of dual and anodal tDCS effects in young adults and help in explaining the great inter-individual variability in response.