Morphological, structural and magnetic properties of Co nanowire/IrMn film heterostructures are studied by atomic force microscopy, non-coplanar X-ray diffraction and magnetization measurements, the latter performed with magnetic field parallel and perpendicular to the nanowire length direction and using remnant (as-grown) and field-cooling protocols. Two magnetic Co phases are established, namely as magnetically-hard hcp phase and soft fcc one (the amount of the latter increasing with the nanowires’ thickness). The magnetization hysteresis loops of these heterostructures present exchange bias, with field shift initially increasing up to a certain Co thickness, followed by a gradual decrease, an effect correlated with changes in the interface energy and shape of the nanowires. The experimental hysteresis loops are successfully reproduced using a modified polycrystalline model for exchange bias, taking into consideration dipolar interactions among the nanowires. Our results are shown that the competitions between anisotropies and dipolar interactions play important roles in the coherent magnetization reversal processes observed.