Sung melody provides a mnemonic cue that can enhance the acquisition of novel verbal material in healthy subjects. Recent evidence suggests that also stroke patients, especially those with mild aphasia, can learn and recall novel narrative stories better when they are presented in sung than spoken format. Extending this finding, the present study explored the cognitive mechanisms underlying this effect by determining whether learning and recall of novel sung vs. spoken stories show a differential pattern of serial position effects (SPEs) and chunking effects in non-aphasic and aphasic stroke patients (N = 31) studied 6 months post-stroke. The structural neural correlates of these effects were also explored using voxel-based morphometry (VBM) and deterministic tractography (DT) analyses of structural MRI data. Non-aphasic patients showed more stable recall with reduced SPEs in the sung than spoken task, which was coupled with greater volume and integrity (indicated by fractional anisotropy, FA) of the left arcuate fasciculus. In contrast, compared to non-aphasic patients, the aphasic patients showed a larger recency effect (better recall of the last vs. middle part of the story) and enhanced chunking (larger units of correctly recalled consecutive items) in the sung than spoken task. In aphasics, the enhanced chunking and better recall on the middle verse in the sung vs. spoken task correlated also with better ability to perceive emotional prosody in speech. Neurally, the sung > spoken recency effect in aphasic patients was coupled with greater grey matter volume in a bilateral network of temporal, frontal, and parietal regions and also greater volume of the right inferior fronto-occipital fasciculus (IFOF). These results provide novel cognitive and neurobiological insight on how a repetitive sung melody can function as a verbal mnemonic aid after stroke.