Statistical learning can be used to gain sensitivity to many important regularities in our environment, including structure that is foundational to language and visual perception. As yet, little is known about how statistical learning takes place in the human brain, especially in children's developing brains and with regard to the broader neurobiology of learning and memory. We therefore explored the relationship between statistical learning and the thickness and volume of structures that are traditionally implicated in declarative and procedural memory, focusing specifically on the left inferior PFC, the hippocampus, and the caudate during early childhood (ages 5–8.5 years). We found that the thickness of the left inferior frontal cortex and volume of the right hippocampus predicted statistical learning ability in young children. Importantly, these regions did not change in thickness or volume with age, but the relationship between learning and the right hippocampus interacted with age such that older children's hippocampal structure more strongly predicted performance. Overall, the data show that children's statistical learning is supported by multiple neural structures that are more broadly implicated in learning and memory, especially declarative memory (hippocampus) and attention/top–down control (the PFC).