To acquire language, infants must learn how to identify words and linguistic structure in speech. Statistical learning has been suggested to assist both of these tasks. However, infants’ capacity to use statistics to discover words and structure together remains unclear. Further, it is not yet known how infants' statistical learning ability relates to their language development. We trained 17-month-old infants on an artificial language comprising non- adjacent dependencies, and examined their looking times on tasks assessing sensitivity to words and structure using an eye-tracked head-turn-preference paradigm. We measured infants’ vocabulary size using a Communicative Development Inventory (CDI) concurrently and at 19, 21, 24, 25, 27, and 30 months to relate performance to language development. Infants could segment the words from speech, demonstrated by a significant difference in looking times to words versus part-words. Infants’ segmentation performance was significantly related to their vocabulary size (receptive and expressive) both currently, and over time (receptive until 24 months, expressive until 30 months), but was not related to the rate of vocabulary growth. The data also suggest infants may have developed sensitivity to generalised structure, indicating similar statistical learning mechanisms may contribute to the discovery of words and structure in speech, but this was not related to vocabulary size.