The order-disorder transition in Ni-Al alloys under irradiation represents an interplay between various reordering processes and disordering due to thermal spikes generated by incident high energy particles. Typically, ordering is enabled by diffusion of thermally generated vacancies, and can only take place at temperatures where they are mobile and in sufficiently high concentration. Here, in situ transmission electron micrographs reveal that the presence of He-usually considered to be a deleterious immiscible atom in this material-promotes reordering in Ni_{3}Al at temperatures where vacancies are not effective ordering agents. A rate-theory model is presented, that quantitatively explains this behavior, based on parameters extracted from atomistic simulations. These calculations show that the V_{2}He complex is an effective agent through its high stability and mobility. It is surmised that immiscible atoms may stabilize reordering agents in other materials undergoing driven processes, and preserve ordered phases at temperature where the driven processes would otherwise lead to disorder.