The group, headed up by cable TV tycoon John Malone, bought the sport from London-based firm CVC Capital Partners.
However, Bernie Ecclestone will still remain in place as CEO and charged with running the sport on a daily basis.
The 85-year-old will work alongside Chase Carey, who will become the new chairman of Formula One.
Ecclestone said: “I would like to welcome Liberty Media and Chase Carey to Formula One and I look forward to working with them.”
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Greg Maffei, President and Chief Executive Officer of Liberty Media, added: “We are excited to become part of Formula One.
“We think our long-term perspective and expertise with media and sports assets will allow us to be good stewards of Formula One and benefit fans, teams and our shareholders.”
SunSport looks at the details and what it means for the sport
What has happened?
Liberty Media, sometimes called just Liberty, have purchased shares from Formula One’s current owners, CVC Capital Partners, who own the majority stake in the sport at 35.5 per cent.
Who are Liberty Media?
A large American company who own a range of media, communications and entertainment businesses, including shares in Time Warner and Viacom, and the Atlanta Braves Major League baseball club.
Who is behind it?
Cable TV king Dr John C Malone. A largely publicity-shy tycoon who is estimated to be worth $7.1billion.
The 75 year old started his career working at Bell Telephone Laboratories and is now the largest individual private landowner in the US, owning 2.2million acres.
JOHN MALONE FACTFILE
Worth: $7.1 billion
Early career: Started working at Bell Telephone Laboratories in economic planning and research and development.
Late career: He worked his way up to President and CEO of Tele-Communications Inc and is now chairman of Liberty Media, Liberty Global, and Liberty Interactive.
Other interests: He is the US’s largest private land owner with 2.2million acres of land.
Nickname: Once dubbed “Darth Vader” by politician Al Gore for his ruthless brokering or cable deals.
Why do Liberty want F1?
Liberty have achieved much success through their Eurosport and Discovery channels and could see F1 as another major opportunity. The sport is crying out for an overhaul and yet it currently makes CVC money.
Liberty, who also own a stake in Formula E, will presumably look to open the American market.
Does this mean the end for Bernie Ecclestone?
Not yet. Ecclestone, 85, still has 14 per cent share – five per cent in his own right and nine per cent through Bambino, his family trust.
The Brit is still a key figure in the sport and will be kept on as the Formula One Group’s CEO.
Does he not run F1?
Yes. He is employed by CVC to run F1 on a day to day basis. Ecclestone has brokered the biggest deals in the sport for 40 years.
Will there be changes to F1?
Initially, the impact will be minimal but F1 teams are open to new owners coming into the sport and helping it grow to a wider global TV audience.
Teams were also critical of CVC for taking profits from the sport.