The charge-changing cross sections \({\sigma }_\textrm{CC}\) have emerged as a promising observable for deducing nuclear charge radii of unstable nuclei. In this study, we measured \({\sigma }_\textrm{CC}\) for neutron-rich nickel isotopes \(^{58\text {--}77}\) Ni at 250 MeV/u. The experimental results were analyzed by using a Glauber model including charged-particle evaporation effects, and the consistency between the measured \(\sigma _\textrm{CC}\) and existing charge radii was investigated. The results demonstrate that the present approach provides a reliable description of \(\sigma _\textrm{CC}\) systematics in the Ni isotopic chain. These findings support the applicability of \(\sigma _\textrm{CC}\) measurements as an alternative probe of charge radii, particularly for nuclei where direct measurements are not available.