The quest for multiferroic materials with ferroelectric and ferromagnetic properties at room temperature continues to be fuelled by the promise of novel devices. Moreover, being able to tune the electrical polarization and the paramagnetic-to-ferromagnetic transition temperature constitutes another current research direction of fundamental and technological importance. Here we report on the first-principles-based prediction of a specific class of materials--namely, R2NiMnO6/La2NiMnO6 superlattices where R is a rare-earth ion--that exhibit an electrical polarization and strong ferromagnetic order near room temperature, and whose electrical and ferromagnetic properties can be tuned by means of chemical pressure and/or epitaxial strain. Analysis of the first-principles results naturally explains the origins of these highly desired features.