The aim of this research was to test the possible effects of cognitive–motor training (CMT) on athletes’ sport performance and cognitive functions. Namely, specific athletic tests, brain processes associated with anticipatory event-related potential (ERP) components and behavioral performance during a cognitive discrimination response task were evaluated pre- and post-training. Twenty-four young semi-professional basketball players were recruited for the study and randomly divided into an experimental (Exp) group executing the CMT training and a control (Con) group performing standard motor training. The CMT training protocol included exercises in which participants performed cognitive tasks during dribbling exercises using interactive devices which emitted visual and auditory stimuli, in which athletes’ responses were recorded. Results showed that following training, only the Exp group improved in all sport-specific tests (17%) and more than the Con group (88% vs. 60%) in response accuracy during the cognitive test. At brain level, post-training anticipatory cognitive processes associated with proactive inhibition and top-down attention in the prefrontal cortex were earlier and heightened in the Exp group. Our findings confirm previous studies on clear improved efficacy of CMT training protocols on sport performance and cognition compared to training based on motor exercises only, but extend the literature in showing that these effects might be explained by enhanced anticipatory brain processing in the prefrontal cortex. The present study also suggests that in order to achieve specific athletic goals, the brain adapts cognitive functions by means of neuroplasticity processes.