Sequence divergence of cis-regulatory elements drives species-specific traits, but how this manifests in the evolution of the neocortex at the molecular and cellular level remains to be elucidated. We investigated the gene regulatory programs in the primary motor cortex of human, macaque, marmoset, and mouse with single-cell multiomics assays, generating gene expression, chromatin accessibility, DNA methylome, and chromosomal conformation profiles from a total of over 180,000 cells. For each modality, we determined species-specific, divergent, and conserved gene expression and epigenetic features at multiple levels. We find that cell type-specific gene expression evolves more rapidly than broadly expressed genes and that epigenetic status at distal candidate cis-regulatory elements (cCREs) evolves faster than promoters. Strikingly, transposable elements (TEs) contribute to nearly 80% of the human-specific cCREs in cortical cells. Through machine learning, we develop sequence-based predictors of cCREs in different species and demonstrate that the genomic regulatory syntax is highly preserved from rodents to primates. Lastly, we show that epigenetic conservation combined with sequence similarity helps uncover functional cis-regulatory elements and enhances our ability to interpret genetic variants contributing to neurological disease and traits.