Living cells regulate many of their vital functions through dynamic, membraneless compartments that phase separate (condense) in response to different types of stimuli. In synthetic cells, responsive condensates could similarly play a crucial role in sustaining their operations. Here we use DNA nanotechnology to design and characterize artificial condensates that respond to light. These condensates form via the programmable interactions of star-shaped DNA subunits (nanostars), which are engineered to include photo-responsive protection domains. In the absence of UV irradiation, the nanostar interactions are not conducive to the formation of condensates. UV irradiation cleaves the protection domains, increases the nanostar valency and enables condensation. We demonstrate that this approach makes it possible to tune precisely the kinetics of condensate formation by dosing UV exposure time. Our experimental observations are complemented by a computational model that characterizes phase transitions of mixtures of particles of different valency, under changes in the mixture composition and bond interaction energy. In addition, we illustrate how UV activation is a useful tool to control the formation and size of DNA condensates in emulsion droplets, as a prototype organelle in a synthetic cell. This research expands our capacity to remotely control the dynamics of DNA-based components via physical stimuli and is particularly relevant to the development of minimal artificial cells and responsive biomaterials.