The discovery of words in continuous speech is one of the first challenges faced by infants during language acquisition. This process is partially facilitated by statistical learning, the ability to discover and encode relevant patterns in the environment. Here, we used an EEG index of neural entrainment in 6-month-olds (n=25) to track their segmentation of words from continuous speech. Infants showed neural entrainment to embedded words that increased logarithmically over the learning period, consistent with a perceptual shift from isolated syllables to word-like units. Moreover, infants’ neural entrainment during learning predicted post-learning behavioural measures of word discrimination (n=18). Finally, the logarithmic increase in entrainment to words was comparable in infants and adults, suggesting that infants and adults follow similar learning trajectories when tracking probability information among speech sounds. Statistical learning effects in infants and adults may reflect overlapping neural mechanisms, which emerge early in life and are maintained throughout the lifespan.