Heterochromatin mainly comprises repeated DNA sequences that are prone to ectopic recombination. In Drosophila cells, 'safe' repair of heterochromatic double-strand breaks by homologous recombination relies on the relocalization of repair sites to the nuclear periphery before strand invasion. The mechanisms responsible for this movement were unknown. Here we show that relocalization occurs by directed motion along nuclear actin filaments assembled at repair sites by the Arp2/3 complex. Relocalization requires nuclear myosins associated with the heterochromatin repair complex Smc5/6 and the myosin activator Unc45, which is recruited to repair sites by Smc5/6. ARP2/3, actin nucleation and myosins also relocalize heterochromatic double-strand breaks in mouse cells. Defects in this pathway result in impaired heterochromatin repair and chromosome rearrangements. These findings identify de novo nuclear actin filaments and myosins as effectors of chromatin dynamics for heterochromatin repair and stability in multicellular eukaryotes.