Recent findings indicate that measures derived from resting-state magnetoencephalography (rsMEG) are sensitive to cortical dysfunction in post-stroke aphasia. Spectral power and multiscale entropy (MSE) measures show that left-hemispheric areas surrounding the stroke lesion (perilesional) exhibit pathological oscillatory slowing and alterations in signal complexity. In the current study, we tested whether individually-targeted high-definition transcranial direct current stimulation (HD-tDCS) can reduce MEG abnormalities and transiently improve language performance. In eleven chronic aphasia survivors, we devised a method to localize perilesional areas exhibiting peak MSE abnormalities, and subsequently targeted these areas with excitatory/anodal-tDCS, or targeted the contralateral homolog areas with inhibitory/cathodal-tDCS, based on prominent theories of stroke recovery. Pathological MEG slowing in these patients was correlated with aphasia severity. Sentence/phrase repetition accuracy was assessed before and after tDCS. A delayed word reading task was administered inside MEG to assess tDCS-induced neurophysiological changes in relative power and MSE computed on the pre-stimulus and delay task time windows. Results indicated increases in repetition accuracy, decreases in contralateral theta (4–7 Hz) and coarse-scale MSE (slow activity), and increases in perilesional low-gamma (25–50 Hz) and fine-scale MSE (fast activity) after anodal-tDCS, indicating reversal of pathological abnormalities. RsMEG may be a sensitive measure for guiding therapeutic tDCS.