Many studies reported a positive relationship between motor skills, cognitive functions, and school performance in school-age children; however, little is known in preschool children. The aim of the present study was to demonstrate the effectiveness of a physical education program (PEP) on locomotor, object control skills, and pre-literacy cognitive functions in a wide population of preschoolers and verify whether weight status could influence these abilities. In the context of the Training-to-Health Project, a sample of 1,029 preschoolers was recruited in kindergartens from the urban area of Palermo (Italy). Their gross motor and pre-literacy skills were tested before (PRE) and after (POST) following 16 weeks (2 h/week) of a PEP, which included ludic-motor activities aimed at developing body awareness and fundamental motor and perceptual-sensory skills. Analyses of variance (ANOVA) were performed to assess the skills before and after the intervention and to evaluate the effect of different categories of weight status on the examined variables. Regression analyses were conducted to confirm the hypothesized interrelationship between motor and pre-literacy skills in the considered sample. Both locomotor/object control and pre-literacy skills were significantly higher in children after the PEP (p < 0.05). We found 23% of overweight children and no significant difference between weight status classes in both PRE and POST PEP groups. In the POST group, higher locomotor and object control skills were mostly associated with better pre-literacy skills. This study shows that PEP was effective in improving both motor and pre-literacy skills in preschoolers independently from age and gender, while weight status did not affect these skills suggesting that this program can be administrated indifferently in children with different categories of weight status. Therefore, PEP could be a decisive education strategy to enhance motor and cognitive learning in preschool children and to achieve successful academic outcomes.