Abstract <p>The isotopic shifts of the 5s ²S_1/2–5p ²P_1/2 cooling transition, the 5p ²P_1/2–4d ²D_3/2 pumping transition, and the 5s ²S_1/2–4d ²D_5/2 electroquadrupole transition are measured in monoisotopic clouds of strontium ions: ⁸⁸Sr⁺, ⁸⁶Sr⁺, and ⁸⁴Sr⁺. To the best of our knowledge, the isotopic shift of the clock transition at 674 nm in ⁸⁴Sr⁺ is measured for the first time and is found to be 1186.7(7.2) MHz. The obtained experimental data is used to construct a King diagram, which allows the field (<i>F</i>) and mass (<i>K</i>) shift constants to be estimated for the transition at a wavelength of 674 nm. The obtained results can be used to test atomic structure calculations, sympathetic cooling, and quantum algorithms.</p>