Forming atomic-scale contacts with attractive geometries and material compositions is a long-term goal of nanotechnology. Here, we show that a rich family of bimetallic atomic-contacts can be fabricated in break-junction setups. The structure and material composition of these contacts can be controlled by atomically precise electromigration, where the metal types of the electron-injecting and sink electrodes determine the type of atoms added to, or subtracted from, the contact structure. The formed bimetallic structures include, for example, platinum and aluminum electrodes bridged by an atomic chain composed of platinum and aluminum atoms as well as iron-nickel single-atom contacts that act as a spin-valve break junction without the need for sophisticated spin-valve geometries. The versatile nature of atomic contacts in bimetallic junctions and the ability to control their structure by electromigration can be used to expand the structural variety of atomic and molecular junctions and their span of properties.