We examined the influence of dysfunctional, non-lesional white matter on cognitive performance in multiple sclerosis (MS). Forty-six MS subjects were assessed using MRI-based myelin water imaging (MWI), and average myelin water fraction (MWF) values across 20 white matter regions of interest (ROIs) were determined. A data-fusion method, multiset canonical correlation analysis (MCCA), was used to investigate the multivariate, deterministic joint relations between MWF, executive function, and demographic and clinical characteristics. MCCA revealed one significant component (p = 0.009) which consisted of three linked profiles, with a pairwise correlation between the MWF and cognitive profiles of r = 0.37, a correlation between MWF and demographics profiles of r = 0.31, and between cognitive and demographics profiles r = 0.64. White matter ROIs representing long-range intra-hemispheric tracts and ROIs connecting the two hemispheres were positively related through their individual profiles to overall cognitive performance, education and female gender, while age, EDSS, and disease duration were related negatively. Surprisingly, lesions within the ROIs had a negligible effect on overall relations between imaging, cognitive, and demographic variables. These findings indicate that there is a strong association between a pattern of MWF values and cognitive performance in MS, which is modulated by age, education, and disease severity. Moreover, this consistent relation involves multiple white matter regions and is separate from the influence of lesions.