Background Computerized training in persons with multiple sclerosis (PwMS) seems to enhance working memory (WM)/information processing (IP), but factors associated with the efficacy of the treatment have not been sufficiently explored. Objective: To identify clinical and radiological characteristics associated with positive WM/IP training responses. Methods Radiological and neuropsychological assessments were carried out on a sample of 35 PwMs who were divided into “WM/IP-impaired” and “WM/IP-preserved.” All participants underwent adaptive n-back training for 10 days and were assessed post-training. Between-group differences (“WM/IP-impaired” vs. “WM/IP-preserved”) in training-induced cognitive improvement were assessed and exploratory correlational/ regression-based methods were employed to assess the relationship between cognitive improvement and clinical and radiological variables. Results All PwMS exhibited WM/IP benefits after training, but those with preserved WM/IP functions showed greater positive effects as well as transfer effects to other WM/IP tests when compared to the impaired group. Additional analyses revealed that positive response to treatment was associated with WM/IP baseline capabilities and greater gray matter volume (GMVOL) in relevant areas such as the thalamus. Conclusions Restorative cognitive training is suitable to improve cognition in PwMS but its effective outcome differs depending on the baseline WM/IP capabilities and GMVOL.