Brawn has been named managing director, motorsports by Liberty as part of the restructure that includes Bernie Ecclestone's ousting as chief executive.
The 62-year-old won 19 world titles across stints with Williams, Benetton, Ferrari and his own Brawn GP outfit, and left F1 at the end of the 2013 season after four years with Mercedes.
Brawn said: "It's fantastic to be returning to the world of Formula 1.
"I've enjoyed consulting with Liberty Media these last few months and I'm looking forward to working with Chase [Carey], Sean [Bratches] and the rest of the Formula 1 team to help the evolution of the sport.
"We have an almost unprecedented opportunity to work together with the teams and promoters for a better F1 for them and, most importantly, for the fans."
Chairman Chase Carey, Ecclestone's successor as CEO, said: "I am delighted to welcome Ross back to Formula 1.
"In his 40 years in the sport, he's brought his magic touch to every team with which he has worked, has almost unparalleled technical knowledge, experience and relationships, and I have already benefitted greatly from his advice and expertise."
Brawn will be joined by former ESPN executive vice president of sales and marketing Sean Bratches, who takes on the role of managing director, commercial operations.
"I am thrilled Sean is joining Formula 1," Carey said.
"Sean was a driving force in building ESPN into one of the world's leading sports franchises.
"His expertise and experience in sales, marketing, digital media, and distribution will be invaluable as we grow Formula 1.
"I look forward to working with Ross and Sean, as well as key current executives including Duncan Llowarch our CFO and Sacha Woodward Hill, our general counsel, the FIA, [F1 chairman emeritus] Bernie and Liberty as we work together to make Formula 1 the best it can be for the teams, promoters and fans for years to come."
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