The development of materials that are non-magnetic in the bulk but exhibit two-dimensional (2D) magnetism at the surface is at the core of spintronics applications. Here, we present the valence-fluctuating material EuIr₂Si₂, where in contrast to its non-magnetic bulk, the Si-terminated surface reveals controllable 2D ferromagnetism. Close to the surface the Eu ions prefer a magnetic divalent configuration and their large 4f moments order below 48 K. The emerging exchange interaction modifies the spin polarization of the 2D surface electrons originally induced by the strong Rashba effect. The temperature-dependent mixed valence of the bulk allows to tune the energy and momentum size of the projected band gaps to which the 2D electrons are confined. This gives an additional degree of freedom to handle spin-polarized electrons at the surface. Our findings disclose valence-fluctuating rare-earth based materials as a very promising basis for the development of systems with controllable 2D magnetic properties which is of interest both for fundamental science and applications.