Grain boundaries (GBs) are a class of defects that directly influence properties of materials. Segregation of solutes to GBs can invoke GB phase transitions and can alter mechanical performance as well as decohesion strength. Consequently, understanding the influence of alloying to GBs plays a vital role in designing tailored materials. In this work, the Σ7 [0001] | 21.78° (sym. plane 12-30) GB in hcp Mg is investigated, following experimental results from high-resolution transition electron microscopy (HR-TEM) that show segregation of Ga to this GB. For the two known configurations of this GB, A and T type, ab-initio simulations are performed as a function of stress and temperature (within the quasi-harmonic approximation) to show the presence of a phase transformation. To study the influence of Ga, a complete set of Ga configurations at the GB is pre-screened employing an empirical potential. After upscaling to accurate ab-initio calculations for the low-energy configurations, the defect phase diagram for the Mg Σ7 GB as a function of the Ga chemical potential is constructed. Ga triggers a transformation between T and A type, and induces a systematic transition of the preferred segregation sites, beyond the dilute limit. The results are qualitatively in very good agreement with our experimental findings based on High Resolution Transmission Electron Microscopy (HR-TEM), in which not only the structural transformation after Ga incorporation is observed. Depending on the processing of the samples and the resulting coverage, there are also different periodic arrangements of Ga atoms at the Mg Σ7 GB observed. Physical mechanisms are provided to explain remaining discrepancies between theory and experiment. The connection to the mechanical performance is demonstrated by studying the work of separation for various configurations and therewith revealing the influence of these configurations on the embrittlement behaviour.