UV/Fe3+ and persulfate are two promising advanced oxidative degradation systems for in situ remediation of perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS), yet a lack of comprehensive understanding of the degradation mechanisms. For the first time, we used density functional theory (DFT) to calculate the entire reaction pathways of the degradation of PFOA/PFOS in water by UV/Fe3+ and persulfate. In addition, we have deeply explored the different attack pathways driven by •OH and SO4−•, and found that SO4−• determines PFOA/PFOS to obtain PFOA/PFOS free radicals through single electron transfer to initiate the degradation reaction, while •OH determines the speed of PFOA/PFOS degradation reaction. Both degradation reactions were thermodynamically advantageous and kinetically feasible under calculated conditions. Based on the thermodynamic data, persulfate was found to be more favorable for the advanced oxidative degradation of Perfluorinated compounds (PFCs). Moreover, for SO4−• and •OH co-existing in the persulfate system, pH will affect the presence and concentration of these two types of free radicals, and low pH is not necessary for the degradation of PFOA/PFOS in the persulfate system. These results can considerably advance our understanding of the PFOA/PFOS degradation process in advanced oxidation processes (AOPs), which is driven by •OH and SO4−•. This study provides a DFT calculation process for the mechanism calculation of advanced oxidation degradation of other types of PFCs pollutants, hoping to elucidate the future development of PFCs removal. Further research should focus on determining the advanced oxidation degradation pathways of other types of PFCs, to support the development of computational studies on the advanced oxidation degradation of PFCs.