Noncoding DNA is central to our understanding of human gene regulation and complex diseases^1,2, and measuring the evolutionary sequence constraint can establish the functional relevance of putative regulatory elements in the human genome^3–9. Identifying the genomic elements that have become constrained specifically in primates has been hampered by the faster evolution of noncoding DNA compared to protein-coding DNA¹⁰, the relatively short timescales separating primate species¹¹, and the previously limited availability of whole-genome sequences¹². Here we construct a whole-genome alignment of 239 species, representing nearly half of all extant species in the primate order. Using this resource, we identified human regulatory elements that are under selective constraint across primates and other mammals at a 5% false discovery rate. We detected 111,318 DNase I hypersensitivity sites and 267,410 transcription factor binding sites that are constrained specifically in primates but not across other placental mammals and validate their cis-regulatory effects on gene expression. These regulatory elements are enriched for human genetic variants that affect gene expression and complex traits and diseases. Our results highlight the important role of recent evolution in regulatory sequence elements differentiating primates, including humans, from other placental mammals.