Background The first years of relapsing-remitting multiple sclerosis (RRMS) constitute the most vulnerable phase for the progression of cognitive impairment (CImp), due to a gradual decrease of compensatory mechanisms. In the first 10 years of RRMS, the temporal volumetric changes of deep gray matter structures must be clarified, since they could constitute reliable cognitive biomarkers for diagnostic, prognostic, and therapeutic purposes. Methods Forty-five cognitively asymptomatic patients with RRMS lasting ≤ 10 years, and with a brain MRI performed in a year from the neuropsychological evaluation (Te-MRI), were included. They performed the Brief International Cognitive Assessment battery for MS. Thirty-one brain MRIs performed in the year of diagnosis (Td-MRI) and 13 brain MRIs of age-and sex-matched healthy controls (HCs) were also included in the study. The relationships between clinical features, cognitive performances, and Te-and Td-MRI volumes were statistically analyzed. Results Cognitively preserved (CP) patients had significantly increased Td-L-putamen (P = 0.035) and Td-R-putamen volume (P = 0.027) with respect to cognitively impaired (CI) ones. CI patients had significantly reduced Te-L-hippocampus (P = 0.019) and Te-R-hippocampus volume (P = 0.042) compared, respectively, with Td-L-hippocampus and Td-R-hippocampus volume. Td-L-putamen volume (P = 0.011) and Te-L-hippocampus volume (P = 0.023) were independent predictors of the Symbol Digit Modalities Test score in all patients (r2 = 0.31, F = 6.175, P = 0.001). Conclusion In the first years of RRMS, putamen hypertrophy and hippocampus atrophy could represent promising indices of cognitive performance and reserve, and become potentially useful tools for diagnostic, prognostic, and therapeutic purposes.