ABSTRACT We measure the colour evolution and quenching time-scales of z = 1.0–1.8 galaxies across the green valley. We derive rest-frame NUVrK colours and select blue-cloud, green-valley, and red-sequence galaxies from the spectral energy distribution modelling of CANDELS GOODS-South and UDS multiband photometry. Separately, we constrain the star-formation history (SFH) parameters (ages, τ) of these galaxies by fitting their deep archival HST grism spectroscopy. We derive the galaxy colour–age relation and show that only rapidly evolving galaxies with characteristic delayed-τ SFH time-scales of <0.5 Gyr reach the red sequence at these redshifts, after a period of accelerated colour evolution across the green valley. These results indicate that the stellar mass build-up of these galaxies stays minimal after leaving the blue cloud and entering the green valley (i.e. it may represent $\lesssim 5{{\ \rm per\ cent}}$ of the galaxies’ final, quiescent masses). Visual inspection of age-sensitive features in the stacked spectra also supports the view that these galaxies follow a quenching sequence along the blue-cloud → green-valley → red-sequence track. For this rapidly evolving population, we measure a green-valley crossing time-scale of $0.99^{+0.42}_{-0.25}$ Gyr and a crossing rate at the bottom of the green valley of $0.82^{+0.27}_{-0.25}$ mag Gyr−1. Based on these time-scales, we estimate that the number density of massive (M⋆ > 1010M⊙) red-sequence galaxies doubles every Gyr at these redshifts, in remarkable agreement with the evolution of the quiescent galaxy stellar mass function. These results offer a new approach to measuring galaxy quenching over time and represent a pathfinder study for future JWST, Euclid, and Roman Space Telescope programs.