Here we present a novel approach to controlling magnetic interactions between atomic-scale nanowires. Our ab initio calculations demonstrate the possibility to tune magnetic properties of Fe nanowires formed on vicinal Cu surfaces. Both intrawire and interwire magnetic exchange parameters are extracted from density functional theory (DFT) calculations. This study suggests that the effective interwire magnetic exchange parameters exhibit Ruderman-Kittel-Kasuya-Yosida-like (RKKY) oscillations as a function of Fe interwire separation. The choice of the vicinal Cu surface offers possibilities for controlling the magnetic coupling. Furthermore, an anisotropic Heisenberg model was used in Monte Carlo simulations to examine the stability of these magnetic configurations at finite temperatures. The predicted critical temperatures of the Fe nanowires on Cu(422) and Cu(533) surfaces are well above room temperature.