Two identical sister copies of eukaryotic chromosomes are synthesized during S phase. To facilitate their recognition as pairs for segregation in mitosis, sister chromatids are held together from their synthesis onward by the chromosomal cohesin complex. Replication fork progression is thought to be coupled to establishment of sister chromatid cohesion, facilitating identification of replication products, but evidence for this has remained circumstantial. Here we show that three proteins required for sister chromatid cohesion, Eco1, Ctf4, and Ctf18, are found at, and Ctf4 travels along chromosomes with, replication forks. The ring-shaped cohesin complex is loaded onto chromosomes before S phase in an ATP hydrolysis-dependent reaction. Cohesion establishment during DNA replication follows without further cohesin recruitment and without need for cohesin to re-engage an ATP hydrolysis motif that is critical for its initial DNA binding. This provides evidence for cohesion establishment in the context of replication forks and imposes constraints on the mechanism involved.