The takeover of the sport was confirmed by Liberty bosses after it was first reported by Sky News City Editor Mark Kleinman.
CVC Capital Partners is handing over its ownership after taking a controlling stake in 2005.
Liberty is backed by American media tycoon John Malone.
Sources have previously said the takeover will see the sport gain a public stock listing for the first time through a tracking stock called Liberty Media Group.
The takeover will yield a windfall of more than $400m (£300m) for veteran F1 chief executive Bernie Ecclestone, who owns a 5.3% stake.
Ecclestone will remain with F1, it has been confirmed – at least for a transitional period of a few years.
In a statement, he said: “I would like to welcome Liberty Media and Chase Carey to Formula One and I look forward to working with them.”
A frenetic period for the ownership and management of F1 will see Carey, a former DirecTV and News Corporation executive, become chairman.
He continues to serve on the board of Rupert Murdoch’s 21st Century Fox and is also a director of Sky plc, the owner of Sky News.
He said: “I greatly admire Formula One as a unique global sports entertainment franchise attracting hundreds of millions of fans each season from all around the world.
“I see great opportunity to help Formula One continue to develop and prosper for the benefit of the sport, fans, teams and investors alike.”
The deal will take part in two parts.
The first tranche would involve the acquisition of an 18.7% stake of F1 and would not be subject to regulatory conditions.
The remainder of the deal would see Liberty Media Corp acquiring the remaining 81.3% of the company, which would be subject to the approval of certain regulators as well as the FIA, world motorsport’s governing body.
Kleinman, who first broke the news of the impending takeover last month, said: “The overall deal may not be complete for a few months, but there’s no doubt that this is a very significant moment for Formula One.”
News Source SkyNews