Newly copied sister chromatids are tethered together by the cohesin complex, but how sister chromatid cohesion coordinates with DNA replication is poorly understood. Prevailing models suggest that cohesin complexes, bound to DNA before replication, remain behind the advancing replication fork to keep sister chromatids together. By visualizing single replication forks colliding with preloaded cohesin complexes, we find that the replisome instead pushes cohesin to where a converging replisome is met. Whereas the converging replisomes are removed during DNA replication termination, cohesin remains on nascent DNA and provides cohesion. Additionally, we show that CMG (CDC45–MCM2-7–GINS) helicase disassembly during replication termination is vital for proper cohesion in budding yeast. Together, our results support a model wherein sister chromatid cohesion is established during DNA replication termination.