[en] The yield from the ⁵⁸Ni(p,γ)⁵⁹Cu reaction has been measured by detection of annihilation radiation in coincidence from the decay of 82 s ⁵⁹Cu. Both thin (600μg cm^-2) and thick (117 mg cm^-2) targets have been used, the latter being thick enough to stop the proton beam at all incident energies. The cross section calculated from the thin target yield contains much structure and is in reasonably good agreement with previous studies. Thermonuclear reaction rates have been calculated from both thin and thick target yields for tempertures of interest in explosive nucleosynthesis. Both thin and thick target rates are in very good agreement with previous determinations but the thin rates are, on the average, 35% higher than thick target rates. The reaction rate for T₉<=2 is shown to be strongly dependent on a resonance at 931 MeV (center of mass) whose strength is not well known. A set of rates for T₉>=2 for both ground state and stellar reactions based on thin target measurements is recommended and analytic fits to the recommended rates are given. (auth)