(1) Background: the objective of this study was to improve certain psycholinguistic and cognitive skills that are fundamental to the development of the reading process, such as phonological awareness, reading decoding, vocabulary and oral narrative comprehension, through the introduction of an Home Literacy Environment Active (HLE(A)) program that involved 54 participants enrolled in the first and second grades of elementary school (from 6 to 8 years old) in the city of Malaga area. (2) Methods: The central task of the intervention program was for the child to read aloud to an adult in the family for between 10 and 15 min, four days per week. In addition, the school students were evaluated on four occasions, at the beginning and end of each academic year, using the Batería de Evaluación de los Procesos Lectores Revisada, Test para la Detección de la Dislexia en niños and Escala Weschsler de Inteligencia instruments. (3) Results: the results demonstrated the efficacy of the HLE(A) program in the improvement of psycholinguistic and cognitive variables measured and, consequently, to an improvement in reading learning and cognitive development. Ultimately, the scientific literature on the subject and the data from the study led us to suggest that it would not only be beneficial for HLE(A) programs to be instituted in early childhood education stage (up to 6 years of age), but that they should be continued after age 6, in elementary education.