Cohesin is a regulator of genome architecture with roles in sister chromatid cohesion and chromosome compaction. The recruitment and mobility of cohesin complexes on DNA is restricted by nucleosomes. Here, we show that the role of cohesin in chromosome organization requires the histone chaperone FACT ('facilitates chromatin transcription') in Saccharomyces cerevisiae. We find that FACT interacts directly with cohesin, and is dynamically required for its localization on chromatin. Depletion of FACT in metaphase cells prevents cohesin accumulation at pericentric regions and causes reduced binding on chromosome arms. Using the Hi-C technique, we show that cohesin-dependent TAD (topological associated domain)-like structures in G1 and metaphase chromosomes are reduced in the absence of FACT. Sister chromatid cohesion is intact in FACT-depleted cells, although chromosome segregation failure is observed. Our data show that FACT contributes to the formation of cohesin-dependent TADs, thus uncovering a new role for this complex in nuclear organization during interphase and mitotic chromosome folding.