Both emotion and sleep are independently known to modulate declarative memory. Memory can be facilitated by emotion, leading to enhanced consolidation across increasing time delays. Sleep also facilitates offline memory processing, resulting in superior recall the next day. Here we explore whether rapid eye movement (REM) sleep, and aspects of its unique neurophysiology, underlie these convergent influences on memory. Using a nap paradigm, we measured the consolidation of neutral and negative emotional memories, and the association with REM-sleep electrophysiology. Subjects that napped showed a consolidation benefit for emotional but not neutral memories. The No-Nap control group showed no evidence of a consolidation benefit for either memory type. Within the Nap group, the extent of emotional memory facilitation was significantly correlated with the amount of REM sleep and also with right-dominant prefrontal theta power during REM. Together, these data support the role of REM-sleep neurobiology in the consolidation of emotional human memories, findings that have direct translational implications for affective psychiatric and mood disorders.