While converging research suggests that increased white matter hyperintensity load is associated with poorer cognition, and the presence of hypertension is associated with increased white matter hyperintensity load, the relationship among hypertension, cognition and white matter hyperintensities is not well understood. We sought to determine the effect of white matter hyperintensity burden on the relationship between hypertension and cognition in individuals with post-stroke aphasia, with the hypothesis that white matter hyperintensity load moderates the relationship between history of hypertension and cognitive function. Health history, Fazekas scores for white matter hyperintensities and Wechsler Adult Intelligence Scale Matrix Reasoning subtest scores for 79 people with aphasia collected as part of the Predicting Outcomes of Language Rehabilitation study at the Center for the Study of Aphasia Recovery at the University of South Carolina and the Medical University of South Carolina were analysed retrospectively. We found that participants with a history of hypertension had increased deep white matter hyperintensity severity (P < 0.001), but not periventricular white matter hyperintensity severity (P = 0.116). Moderation analysis revealed that deep white matter hyperintensity load moderates the relationship between high blood pressure and Wechsler Adult Intelligence Scale scores when controlling for age, education, aphasia severity and lesion volume. The interaction is significant, showing that a history of high blood pressure and severe deep white matter hyperintensities together are associated with poorer Matrix Reasoning scores. The overall model explains 41.85% of the overall variation in Matrix Reasoning score in this group of participants. These findings underscore the importance of considering cardiovascular risk factors in aphasia treatment, specifically hypertension and its relationship to brain health in post-stroke cognitive function.