That was achieved on Wednesday, during an extraordinary meeting of the World Motor Sport Council in Geneva.
The FIA, which will retain its controversial 1pc ownership share, said it believes Liberty "is clearly well positioned to ensure the continued development of its pinnacle championship".
The future of F1 supremo Bernie Ecclestone, however, is less clear.
As Wednesday's news broke, the Telegraph reported that 86-year-old Ecclestone will be "eased aside" in the new Liberty era.
The newspaper said Ecclestone wanted to keep his role for up to three more years, "but so far all Liberty's rhetoric has been about making a clean break with the past".