Condensin is a structural maintenance of chromosomes (SMC) complex family member thought to build mitotic chromosomes by DNA loop extrusion. However, condensin variants unable to extrude loops, yet proficient in chromosome formation, were recently described. Here, we explore how condensin might alternatively build chromosomes. Using bulk biochemical and single-molecule experiments with purified fission yeast condensin, we observe that individual condensins sequentially and topologically entrap two double-stranded DNAs (dsDNAs). Condensin loading transitions through a state requiring DNA bending, as proposed for the related cohesin complex. While cohesin then favors the capture of a second single-stranded DNA (ssDNA), second dsDNA capture emerges as a defining feature of condensin. We provide complementary invivo evidence for DNA-DNA capture in the form of condensin-dependent chromatin contacts within, as well as between, chromosomes. Our results support a "diffusion capture" model in which condensin acts in mitotic chromosome formation by sequential dsDNA-dsDNA capture.