We present Institut de Radioastronomie Millimétrique Plateau de Bure Interferometer observations of the 12CO (3–2) emission from two far-infrared luminous QSOs at z ∼ 2.5 selected from the Herschel-Astrophysical Tetrahertz Large Area Survey. These far-infrared bright QSOs were selected to have supermassive black holes (SMBHs) with masses similar to those thought to reside in submillimetre galaxies (SMGs) at z ∼ 2.5, making them ideal candidates as systems in the potential transition from an ultraluminous infrared galaxy phase to a submillimetre faint, unobscured, QSO. We detect 12CO (3–2) emission from both QSOs and we compare their baryonic, dynamical and SMBH masses to those of SMGs at the same epoch. We find that these far-infrared bright QSOs have similar dynamical but lower gas masses than SMGs. We combine our results with literature values and find that at a fixed LFIR, far-infrared bright QSOs have ∼50 ± 30 per cent less warm/dense gas than SMGs. Taken together with previous results, which show that QSOs lack the extended, cool reservoir of gas seen in SMGs, this suggests that far-infrared bright QSOs are at a different evolutionary stage. This is consistent with the hypothesis that far-infrared bright QSOs represent a short (∼1 Myr) but ubiquitous phase in the transformation of dust-obscured, gas-rich, starburst-dominated SMGs into unobscured, gas-poor, QSOs.