"F1 has huge potential with multiple untapped opportunities," said new chief executive Chase Carey after ending 86-year-old Ecclestone's 40-year reign on Monday.
"We will work...to enhance the racing experience and add new dimensions to the sport and we look forward to sharing these plans over time."
Carey, appointed Formula One chairman in September after serving as vice-chairman of Rupert Murdoch's 21st Century Fox, and Liberty Media's chief executive Greg Maffei have both said there is a lot they want to do differently.
Maffei has spoken of more races in Latin America, Asia and the United States while Carey has indicated that Liberty wants to safeguard the sport's historic venues in Europe, ramp up marketing efforts and engage the fans more.
There has been talk of treating every race like a Super Bowl, creating a buzz that extends far beyond the racetrack, but without 'Americanising' the sport's fundamentals or alienating the purists.
Liberty Media has plenty of experience and resources, with interests in the Atlanta Braves baseball team, satellite radio service Sirius XM, entertainment group Live Nation and minority interests in Time Warner and Viacom.
Where Ecclestone's business model was based on television rights and ever-increasing hosting fees that have left circuits with little chance of making a profit, Liberty have emphasised a shift towards sustainability and new revenue streams.
"Less than one percent of revenues are from digital," Maffei said in September after Liberty agreed to acquire the commercial rights from CVC Capital Parthers.
"They really have no organised digital effort. I think there's a lot of things that can be done around gaming, VR (virtual reality) and AR (augmented reality).
"There's an enormous amount of video feed and data about the races that we are already capturing that we are not in any way processing incrementally for the dedicated fan," he added.
Where Ecclestone was often at odds with the teams, adopting a divide and rule approach, Carey has sounded more collegiate and inclusive with talk of cost controls and ensuring a fairer share of the spoils.
That will be easier said than done, with the likes of glamour team Ferrari in particular handsomely rewarded for historic performances while smaller teams struggle to survive.
The appointment of Ross Brawn in a management role overseeing motorsport activities has also raised hopes among fans and participants preparing for the first race in Australia in two months' time.
Brawn worked closely at Ferrari with Jean Todt, now the head of the governing FIA, and was also a principal at Honda before leading his own team and then Mercedes.
Zak Brown, the newly-appointed American executive director of McLaren, backed Carey and his team to do what was needed.
"Over the next decade I expect the way Formula One is run will become both freer and more fan-friendly," said Brown.
"Fan engagement is where it's at these days, and it's clear that the Liberty Media guys get that."
(Editing by Amlan Chakraborty)
