Recent work suggests that cultural transmission can lead to the emergence of linguistic structure as speakers’ weak individual biases become amplified through iterated learning. However, to date, no published study has demonstrated a similar emergence of linguistic structure in children. This gap is problematic given that languages are mainly learned by children and that adults may bring existing linguistic biases to the task. Here, we conduct a large-scale study of iterated language learning in both children and adults, using a novel, child-friendly paradigm. The results show that while children make more mistakes overall, their languages become more learnable and show learnability biases similar to those of adults. Child languages did not show a significant increase in linguistic structure over time, but consistent mappings between meanings and signals did emerge on many occasions, as found with adults. This provides the first demonstration that cultural transmission affects the languages children and adults produce similarly.