The E0 transition strength in the 2₂⁺ → 2₁⁺ transitions of ^58,60,62Ni have been determined for the first time following a series of measurements at the Australian National University (ANU) and the University of Kentucky (UK). The CAESAR Compton-suppressed HPGe array and the Super-e solenoid at ANU were used to measure the δ(E2/M1) mixing ratio and internal conversion coefficient of each transition following inelastic proton scattering. Level half-lives, δ(E2/M1) mixing ratios and γ-ray branching ratios were measured at UK following inelastic neutron scattering. The new spectroscopic information was used to determine the E0 strengths. These are the first 2₂⁺ → 2₁⁺ E0 transition strengths measured in nuclei with spherical ground states and the E0 component is found to be unexpectedly large; in fact, these are amongst the largest E0 transition strengths in medium and heavy nuclei reported to date.