The grain boundary (GB) microchemistry and precipitation behaviour in high-strength Al-Zn-Mg-Cu alloys has an important influence on their mechanical and electrochemical properties. Simulation of the GB segregation, precipitation, and solute distribution in these alloys requires an accurate description of the thermodynamics and kinetics of this multi-component system. CALPHAD databases have been successfully developed for equilibrium thermodynamic calculations in complex multi-component systems, and in recent years have been combined with diffusion simulations. In this work, we have directly incorporated a CALPHAD database into a phase-field framework, to simulate, with high fidelity, the complex kinetics of the non-equilibrium GB microstructures that develop in these important commercial alloys during heat treatment. In particular, the influence of GB solute segregation, GB diffusion, precipitate number density, and far-field matrix composition, on the growth of a population of GB η-precipitates, was systematically investigated in a model Al-Zn-Mg-Cu alloy of near AA7050 composition. It is shown that the GB solute distribution in the early stages of ageing was highly heterogeneous and strongly affected by the distribution of GB η-precipitates. Significant Mg and Cu GB segregation was predicted to remain during overageing, while Zn was rapidly depleted. This non-trivial GB segregation behaviour markedly influenced the resulting precipitate morphologies, but the overall precipitate transformation kinetics on a GB were relatively unaffected. Furthermore, solute depletion adjacent to the GB was largely determined by Zn and Mg diffusion, which will affect the development of precipitate free zones during the early stages of ageing. The simulation results were compared with scanning transmission electron microscopy and atom probe tomography characterisation of alloys of the similar composition, with good agreement.