Background: Preterm birth is one of the world’s critical health problems, with an incidence of 5% to 18% of living newborns according to various countries. White matter injuries due to preoligodendrocytes deficits cause hypomyelination in children born preterm. Preterm infants also have multiple neurodevelopmental sequelae due to prenatal and perinatal risk factors for brain damage. The purpose of this work was to explore the effects of the brain risk factors and MRI volumes and abnormalities on the posterior motor and cognitive development at 3 years of age. Methods: A total of 166 preterm infants were examined before 4 months and clinical and MRI evaluations were performed. MRI showed abnormal findings in 89% of the infants. Parents of all infants were invited to receive the Katona neurohabilitation treatment. The parents of 128 infants accepted and received Katona’s neurohabilitation treatment. The remaining 38 infants did not receive treatment for a variety of reasons. At the three-year follow-up, Bayley’s II Mental Developmental Index (MDI) and the Psychomotor Developmental Index (PDI) were compared between treated and untreated subjects. Results: The treated children had higher values of both indices than the untreated. Linear regression showed that the antecedents of placenta disorders and sepsis as well as volumes of the corpus callosum and of the left lateral ventricle significantly predicted both MDI and PDI, while Apgar $<$ 7 and volume of the right lateral ventricle predicted the PDI. Conclusions: (1) The results indicate that preterm infants who received Katona’s neurohabilitation procedure exhibited significantly better outcomes at 3 years of age compared to those who did not receive the treatment. (2) The presence of sepsis and the volumes of the corpus callosum and lateral ventricles at 3–4 months were significant predictors of the outcome at 3 years of age.