ABSTRACT We examine the connection between the properties of the circumgalactic medium (CGM) and the quenching and morphological evolution of central galaxies in the EAGLE and IllustrisTNG simulations. The simulations yield very different median CGM mass fractions, fCGM, as a function of halo mass, M200, with low-mass haloes being significantly more gas-rich in IllustrisTNG than in EAGLE. Nonetheless, in both cases scatter in fCGM at fixed M200 is strongly correlated with the specific star formation rate and the kinematic morphology of central galaxies. The correlations are strongest for ∼L⋆ galaxies, corresponding to the mass scale at which AGN feedback becomes efficient. This feedback elevates the CGM cooling time, preventing gas from accreting on to the galaxy to fuel star formation, and thus establishing a preference for quenched, spheroidal galaxies to be hosted by haloes with low fCGM for their mass. In both simulations, fCGM correlates negatively with the host halo’s intrinsic concentration, and hence with its binding energy and formation redshift, primarily because early halo formation fosters the rapid early growth of the central black hole (BH). This leads to a lower fCGM at fixed M200 in EAGLE because the BH reaches high accretion rates sooner, whilst in IllustrisTNG it occurs because the central BH reaches the mass threshold at which AGN feedback is assumed to switch from thermal to kinetic injection earlier. Despite these differences, there is consensus from these state-of-the-art simulations that the expulsion of efficiently cooling gas from the CGM is a crucial step in the quenching and morphological evolution of central galaxies.