Directed differentiation from human pluripotent stem cells (hPSCs) has seen significant progress in recent years. However, most differentiated populations exhibit immature properties of an early embryonic stage, raising concerns about their ability to model and treat disease. Here, we report the directed differentiation of hPSCs into medial ganglionic eminence (MGE)-like progenitors and their maturation into forebrain type interneurons. We find that early-stage progenitors progress via a radial glial-like stem cell enriched in the human fetal brain. Both in vitro and posttransplantation into the rodent cortex, the MGE-like cells develop into GABAergic interneuron subtypes with mature physiological properties along a prolonged intrinsic timeline of up to 7 months, mimicking endogenous human neural development. MGE-derived cortical interneuron deficiencies are implicated in a broad range of neurodevelopmental and degenerative disorders, highlighting the importance of these results for modeling human neural development and disease.