Over the past 10 Gyr, star-forming galaxies have changed dramatically, from clumpy and gas rich, to rather quiescent stellar-dominated discs with specific star formation rates lower by factors of a few tens. We present a general theoretical model for how this transition occurs, and what physical processes drive it, making use of 1D axisymmetric thin disc simulations with an improved version of the Gravitational Instability-Dominated Galaxy Evolution Tool (gidget) code. We show that at every radius galaxies tend to be in a slowly evolving equilibrium state wherein new accretion is balanced by star formation, galactic winds and radial transport of gas through the disc by gravitational instability-driven torques. The gas surface density profile is determined by which of these terms are in balance at a given radius – direct accretion is balanced by star formation and galactic winds near galactic centres, and by transport at larger radii. We predict that galaxies undergo a smooth transition from a violent disc instability phase to secular evolution. This model provides a natural explanation for the high velocity dispersions and large clumps in z ∼ 2 galaxies, the growth and subsequent quenching of bulges, and features of the neutral gas profiles of local spiral galaxies.