Despite that cognitive impairment is a known early feature present in multiple sclerosis (MS) patients, the biological substrate of cognitive deficits in MS remains elusive. In this study, we assessed whether T1 relaxometry, as obtained in clinically acceptable scan times by the recent Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) sequence, may help identifying the structural correlate of cognitive deficits in relapsing-remitting MS patients (RRMS). Twenty-nine healthy controls (HC) and forty-nine RRMS patients underwent high-resolution 3T magnetic resonance imaging to obtain optimal cortical lesion (CL) and white matter lesion (WML) count/volume and T1 relaxation times. T1 z scores were then obtained between T1 relaxation times in lesion and the corresponding HC tissue. Patient cognitive performance was tested using the Brief Repeatable Battery of Neuro-psychological Tests. Multivariate analysis was applied to assess the contribution of MRI variables (T1 z scores, lesion count/volume) to cognition in patients and Bonferroni correction was applied for multiple comparison. T1 z scores were higher in WML (p < 0.001) and CL-I (p < 0.01) than in the corresponding normal-appearing tissue in patients, indicating relative microstructural loss. (1) T1 z scores in CL-I (p = 0.01) and the number of CL-II (p = 0.04) were predictors of long-term memory; (2) T1 z scores in CL-I (β = 0.3; p = 0.03) were independent determinants of long-term memory storage, and (3) lesion volume did not significantly influenced cognitive performances in patients. Our study supports evidence that T1 relaxometry from MP2RAGE provides information about microstructural properties in CL and WML and improves correlation with cognition in RRMS patients, compared to conventional measures of disease burden.