Telomeres are nucleoprotein complexes that protect the ends of chromosomes and are essential for chromosome stability in Eukaryotes. In cells, individual telomeres form distinct globules of finite size that appear to be smaller than expected for bare DNA. Moreover, upon changes in their protein composition, telomeres can cluster to form telomere-induced-foci (TIFs) or co-localize with promyelocytic leukemia (PML) nuclear bodies. The physical basis for collapse of individual telomeres and coalescence of multiple ones remains unclear, as does the relationship between these two phenomena. By combining single-molecule measurements, optical microscopy, turbidity assays, and simulations, we show that the telomere scaffolding protein TRF2 can condense individual DNA chains and drives coalescence of multiple DNA molecules, leading to phase separation and the formation of liquid-like droplets. Addition of the TRF2 binding protein hRap1 modulates phase boundaries and tunes the specificity of solution demixing while simultaneously altering the degree of DNA compaction. Our results suggest that the condensation of single telomeres and formation of biomolecular condensates containing multiple telomeres are two different outcomes driven by the same set of molecular interactions. Moreover, binding partners, such as other telomere components, can alter those interactions to promote single-chain DNA compaction over multiple-chain phase separation.