•Learning two languages from birth has no effect on cortical thickness compared to learning only one language.•In the bilingual brain, the later a second language is acquired the greater the effect on cortical thickness.•In the left inferior frontal gyrus, cortical thickness increases with age of acquisition of second language.•In the right inferior frontal gyrus, cortical thickness decreases with age of acquisition of second language. We examined the effects of learning a second language (L2) on brain structure. Cortical thickness was measured in the MRI datasets of 22 monolinguals and 66 bilinguals. Some bilingual subjects had learned both languages simultaneously (0–3years) while some had learned their L2 after achieving proficiency in their first language during either early (4–7years) or late childhood (8–13years). Later acquisition of L2 was associated with significantly thicker cortex in the left inferior frontal gyrus (IFG) and thinner cortex in the right IFG. These effects were seen in the group comparisons of monolinguals, simultaneous bilinguals and early and late bilinguals. Within the bilingual group, significant correlations between age of acquisition of L2 and cortical thickness were seen in the same regions: cortical thickness correlated with age of acquisition positively in the left IFG and negatively in the right IFG. Interestingly, the monolinguals and simultaneous bilinguals did not differ in cortical thickness in any region. Our results show that learning a second language after gaining proficiency in the first language modifies brain structure in an age-dependent manner whereas simultaneous acquisition of two languages has no additional effect on brain development.