Exonuclease 1 (Exo1) is a 5’→3’ exonuclease and 5’-flap endonuclease that plays a critical role in multiple eukaryotic DNA repair pathways. Exo1 processing at DNA nicks and double-strand breaks creates long stretches of single-stranded DNA, which are rapidly bound by replication protein A (RPA) and other single-stranded DNA binding proteins (SSBs). Here, we use single-molecule fluorescence imaging and quantitative cell biology approaches to reveal the interplay between Exo1 and SSBs. Both human and yeast Exo1 are processive nucleases on their own. RPA rapidly strips Exo1 from DNA, and this activity is dependent on at least three RPA-encoded single-stranded DNA binding domains. Furthermore, we show that ablation of RPA in human cells increases Exo1 recruitment to damage sites. In contrast, the sensor of single-stranded DNA complex 1-a recently identified human SSB that promotes DNA resection during homologous recombination-supports processive resection by Exo1. Although RPA rapidly turns over Exo1, multiple cycles of nuclease rebinding at the same DNA site can still support limited DNA processing. These results reveal the role of single-stranded DNA binding proteins in controlling Exo1-catalyzed resection with implications for how Exo1 is regulated during DNA repair in eukaryotic cells.