Particle irradiation is an effective method for manipulating properties of individual carbon nanotubes (CNTs). This potential, however, remains unexplored for macroscopic assemblies of cross-linked CNTs. Here, we study structural and electrical properties of ultralow-density cross-linked CNT-based nanofoams exposed to ion irradiation at room temperature over a wide range of ion masses and fluences. For all irradiation conditions studied, the electrical resistance of nanofoams initially increases with a rate that scales with the number of ballistically generated displacements. This process is attributed to the buildup of defects in graphitic nanoligaments. Irradiation with Ne and heavier ions leads to a decrease in the electrical resistance at large fluences, which is attributed to radiation-induced foam densification. In addition, heavy-ion bombardment causes amorphization of CNTs and smoothing of ligament surfaces. These results demonstrate that ion bombardment can be used for tailoring density, ligament morphology, and electrical properties of CNT-based foams.