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We use the FIRE-2 cosmological simulations to study the formation of a quasi-static, virial-temperature gas phase in the circumgalactic medium (CGM) at redshifts 0<z<5, and how the formation of this virialized phase affects the evolution of galactic discs. We demonstrate that when the halo mass crosses ~10^12 M_sun, the cooling time of shocked gas in the inner CGM (~0.1 R_vir, where R_vir is the virial radius) exceeds the local free-fall time. The inner CGM then experiences a transition from on average sub-virial temperatures (T<<T_vir), large pressure fluctuations and supersonic inflow/outflow velocities, to virial temperatures (T~T_vir), uniform pressures and subsonic velocities. This transition occurs when the outer CGM (~0.5 R_vir) is already subsonic and has a temperature ~T_vir, indicating that the longer cooling times at large radii allow the outer CGM to virialize at lower halo masses than the inner CGM. This outside-in CGM virialization scenario is in contrast with inside-out scenarios commonly envisioned based on more idealized simulations. We demonstrate that inner CGM virialization coincides with abrupt changes in the central galaxy and its stellar feedback: the galaxy settles into a stable rotating disc, star formation transitions from `bursty' to `steady,' and stellar-driven galaxy-scale outflows are suppressed. Our results thus suggest that CGM virialization is initially associated with the formation of rotation-dominated thin galactic discs, rather than with the quenching of star formation as often assumed.