The Holliday junction (HJ), a cross-shaped structure that physically links the two DNA helices, is a key intermediate in homologous recombination, DNA repair, and replication. Several helicase-like proteins are known to bind HJs and promote their branch migration (BM) by translocating along DNA at the expense of ATP hydrolysis. Surprisingly, the bacterial recombinase protein RecA and its eukaryotic homologue Rad51 also promote BM of HJs despite the fact they do not bind HJs preferentially and do not translocate along DNA. RecA/Rad51 plays a key role in DNA double-stranded break repair and homologous recombination. RecA/Rad51 binds to ssDNA and forms contiguous filaments that promote the search for homologous DNA sequences and DNA strand exchange. The mechanism of BM promoted by RecA/RAD51 is unknown. Here, we demonstrate that cycles of RecA/Rad51 polymerization and dissociation coupled with ATP hydrolysis drives the BM of HJs.