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 $313million. 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 pitwall 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."
Maffei made it clear that he sees Quint as a way for Liberty to expand its interests and monetise its skills across different sports.
"We see both enormous opportunity for them to help us extend our capabilities, and sell to our customers around F1, improve our hospitality experiences," he said. "But also an opportunity to leverage the strengths we have, and sell into other kinds of sports.
"If you look at the high-end experiences that get created in F1, they are relatively unique compared to what you can get in most other sports. We think that opportunity exists to extend that to other sports.
"We think Quint does a great job, and we can help accelerate them. I expect the acquisition will be financially accretive day one, and I expect that Quint will grow faster than F1, with our help."
Quint CEO Brian Ruede agreed that the new partnership would help to transfer F1 knowledge into other sports.
"We could not be more thrilled for the Quint team to join forces with Liberty Media," said Ruede.
"This has been an incredible journey and is a transformative moment for Quint and our position in the experiential and travel economy. Liberty Media is the right partner for our next evolution of growth."