Although DNA replication is a fundamental aspect of biology, it is not known what determines where DNA replication starts and stops in the human genome. We directly identified and quantitatively compared sites of replication initiation and termination in untransformed human cells. We found that replication preferentially initiates at the transcription start site of genes occupied by high levels of RNA polymerase II, and terminates at their polyadenylation sites, thereby ensuring global co-directionality of transcription and replication, particularly at gene 5' ends. During replication stress, replication initiation is stimulated downstream of genes and termination is redistributed to gene bodies; this globally reorients replication relative to transcription around gene 3' ends. These data suggest that replication initiation and termination are coupled to transcription in human cells, and propose a model for the impact of replication stress on genome integrity.