While multiple studies have reported the accelerated evolution of brain gene expression in the human lineage, the mechanisms underlying such changes are unknown. Here, we address this issue from a developmental perspective, by analyzing mRNA and microRNA (miRNA) expression in two brain regions within macaques, chimpanzees, and humans throughout their lifespan. We find that constitutive gene expression divergence (species differences independent of age) is comparable between humans and chimpanzees. However, humans display a 3-5 times faster evolutionary rate in divergence of developmental patterns, compared to chimpanzees. Such accelerated evolution of human brain developmental patterns (i) cannot be explained by life-history changes among species, (ii) is twice as pronounced in the prefrontal cortex than the cerebellum, (iii) preferentially affects neuron-related genes, and (iv) unlike constitutive divergence does not depend on cis-regulatory changes, but might be driven by human-specific changes in expression of trans-acting regulators. We show that developmental profiles of miRNAs, as well as their target genes, show the fastest rates of human-specific evolutionary change, and using a combination of computational and experimental methods, we identify miR-92a, miR-454, and miR-320b as possible regulators of human-specific neural development. Our results suggest that different mechanisms underlie adaptive and neutral transcriptome divergence, and that changes in the expression of a few key regulators may have been a major driving force behind rapid evolution of the human brain.