The deal also gives Liberty a foothold in other sports and major events on the hospitality and entertainment side, including NASCAR's Chicago street race, the NBA, Australian Open tennis and the Kentucky Derby.
The deal to buy "greater than 90%" of Quint, which is expected to be completed before the end of the year, values it at $313m. The two organisations will continue to be run as independent companies.
Quint has gained a lot of momentum within the sport and impressed Liberty by creating F1 Experiences and expanding far beyond the traditional Paddock Club environment, allowing wealthy fans to sit on the pit wall or be entertained in pit garages.
"Quint has done a great job in creating F1 Experiences and their high-end hospitality," said Liberty CEO Greg Maffei.
"Things like giving you an opportunity to have dinner on Thursday night on the track, things like getting garage tours, things like hot laps that allow you to get in cars which are just a step below F1 and have someone drive you around a track and simulate the experience of being an F1 driver.
"All of those things have allowed them to have a great network and a great database of who our high-end customers are, reaching out, knowing how to sell them.
"They've also done that across other sports. They do things like the Kentucky Derby with Churchill Downs. They do the NBA All-Star game, and other sports like that."