The announcement ends years of speculation about the ownership of Formula 1.
Bernie Ecclestone will remain as chief executive but Chase Carey, vice-chairman of 21st Century Fox, will become the new chairman.
Liberty Media has also stakes in several sports and entertainment businesses, including the Atlanta Braves Major League Baseball club.
Owned by the billionaire John Malone, Liberty Media will initially purchase a minority stake in the world’s leading motor-racing championship. A full takeover is planned if regulators approve the deal.
The total transaction values the firm at $8 billion but includes $4.1 billion worth of F1’s debt.
Liberty Media is buying the stake from the private equity firm CVC Capital.
CVC has held a stake for the past decade but sold some of its holding in 2012.
The private equity firm has been criticized for taking considerable profits from the sport, which has suffered from falling TV ratings in recent years.
“We are excited to become part of Formula 1,” said Greg Maffei, chief executive of Liberty Media.
“We think our long-term perspective and expertise with media and sports assets will allow us to be good stewards of Formula 1 and benefit fans, teams and our shareholders.”
Bernie Ecclestone said: “I would like to welcome Liberty Media and Chase Carey to Formula 1 and I look forward to working with them.”
Earlier, the 85-year-old British businessman said in an interview with Reuters that he had been asked to stay on for three years and would miss the Singapore Grand Prix on September 18 as he needed be in London for the negotiations.
Bernie Ecclestone has run the sport for 40 years.
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