Stand-alone hydrogen production from cheap renewable power, notably solar, has received considerable attention as a way to produce fuel and feedstock for a future climate-neutral energy system. Here we assess the integration of green hydrogen production and the deployment of electrolysers with a power system that is progressively decarbonized by the deployment of intermittent renewables, viz. wind and solar. We find that full power system decarbonisation is cost-optimal for a renewable power mix that includes a strong wind component. For this power mix, electrolyser deployment kicks in only at around 70% grid decarbonisation. Beyond this point, electrolyser build-out scales linearly with further renewables deployment. The electrolyser-to-renewables deployment ratio depends strongly on the solar and wind mix but is fairly insensitive to relative costs of electrolysers to renewables. Finally, we find a substantial cost advantage for the coproduction of green power and green hydrogen compared to stand-alone green hydrogen production.