The development of the ability to anticipate—as manifested by preparatory actions and neural activation related to the expectation of an upcoming stimulus—may play a key role in the ontogeny of cognitive skills more broadly. This preregistered study examined anticipatory brain potentials and behavioral responses (reaction time; RT) to anticipated target stimuli in relation to individual differences in the ability to use goals to direct action (as indexed by measures of executive function; EF). A cross‐sectional investigation was conducted in 40 adults (aged 18–25 years) and 40 children (aged 6–8 years) to examine the association of changes in the amplitude of modality‐specific alpha‐range rhythms in the electroencephalogram (EEG) during anticipation of lateralized visual, tactile, or auditory stimuli with inter‐ and intraindividual variation in RT and EF. Children and adults exhibited contralateral anticipatory reductions in the mu rhythm and the visual alpha rhythm for tactile and visual anticipation, respectively, indicating modality and spatially specific attention allocation. Variability in within‐subject anticipatory alpha lateralization (the difference between contralateral and ipsilateral alpha power) was related to single‐trial RT. This relation was more prominent in adults than in children, and was not apparent for auditory stimuli. Multilevel models indicated that interindividual differences in anticipatory mu rhythm lateralization contributed to the significant association with variability in EF, but this was not the case for visual or auditory alpha rhythms. Exploratory microstate analyses were undertaken to cluster global field power (GFP) into a distribution‐free temporal analysis examining developmental differences across samples and in relation to RT and EF. Anticipation is suggested as a developmental bridge construct connecting neuroscience, behavior, and cognition, with anticipatory EEG oscillations being discussed as quantifiable and potentially malleable indicators of stimulus prediction.