High-resolution imaging shows that persistent DNA damage in budding yeast localizes in distinct perinuclear foci for repair. The signals that trigger DNA double-strand break (DSB) relocation or determine their destination are unknown. We show here that DSB relocation to the nuclear envelope depends on SUMOylation mediated by the E3 ligases Siz2 and Mms21. In G1, a polySUMOylation signal deposited coordinately by Mms21 and Siz2 recruits the SUMO targeted ubiquitin ligase Slx5/Slx8 to persistent breaks. Both Slx5 and Slx8 are necessary for damage relocation to nuclear pores. When targeted to an undamaged locus, however, Slx5 alone can mediate relocation in G1-phase cells, bypassing the requirement for polySUMOylation. In contrast, in S-phase cells, monoSUMOylation mediated by the Rtt107-stabilized SMC5/6-Mms21 E3 complex drives DSBs to the SUN domain protein Mps3 in a manner independent of Slx5. Slx5/Slx8 and binding to pores favor repair by ectopic break-induced replication and imprecise end-joining.