The goal of the study is to investigate a correlation between different levels of speech organization, indicating the physiological processes of maturation of the vocal tract structures and brain regions associated with speech and language, and basic electroencephalogram (EEG) rhythms, reflecting the age-related dynamics of maturation of brain structures in children aged 4–11 years. The complex method of analysis, including EEG registration, clinical and spectral analysis of EEG; dichotic listening, identifying the profile of functional lateral asymmetry (PFLA), and phonemic hearing of the child; recording, linguistic, and acoustic analysis of child speech; and identification of speech characteristics reflecting the formation of its different levels, was used. Two complementary experimental series were conducted: the correlation between EEG parameters, speech features, dichotic listening, the PFLA, and phonemic hearing of the child in the age dynamics of 4–11 years (first); the specificity of EEG patterns in children at different stages of reading skills formation (second). The result of this study showed the correlation between acoustic and linguistic features of child speech and brain activity. The analysis of EEG and acoustic features of child speech revealed the correlation between pitch and pitch range values in spontaneous speech and theta-rhythm intensity in EEG. High values of pitch and its variation in younger children (4–6 years) are related to the intensity of theta rhythm in the EEG pattern, as this rhythm is most expressed in younger children. It was revealed that the alpha rhythm is asymmetrically localized in children with clear pronunciation of words (which determines the intelligibility of their speech) that is typical for 6.5- to 11-year-old children. The formation of reading skills in a child is associated with a change in the characteristics of the alpha rhythm—from irregular, unstable, low frequency, and low amplitude in children at the beginning of reading skills mastering to medium and low amplitude, regular, asymmetrically localized in children reading words and phrases. The specifics of the relation between brain activity and different levels of speech formation at different child’s age periods are discussed.