Chase Carey, vice chairman of 21st Century Fox, has been appointed to succeed the 86-year-old, although Ecclestone has been given an honorary role as chairman emeritus and will serve as an adviser to the new board.
"I'm proud of the business that I built over the last 40 years and all that I have achieved with Formula One," Ecclestone said in a statement released by Liberty Media.
"And would like to thank all of the promoters, teams, sponsors and television companies that I have worked with.
"I'm very pleased that the business has been acquired by Liberty and that it intends to invest in the future of F1. I am sure that Chase will execute his role in a way that will benefit the sport."
Liberty Media also confirmed it would soon be renamed the Formula One Group after it completed the acquisition of 100% of F1's shares from the consortium led by private equity firm CVC -- a takeover process which began in September
. Liberty said then that Ecclestone would continue as CEO for three years.
The 62-year-old Carey will have the title of chief executive added to his existing role as chairman.
"I am excited to be taking on the additional role of CEO," he said. "F1 has huge potential with multiple untapped opportunities.
"I have enjoyed hearing from the fans, teams, FIA, promoters and sponsors on their ideas and hopes for the sport.
"We will work with all of these partners to enhance the racing experience and add new dimensions to the sport and we look forward to sharing these plans overtime."
Ecclestone's position at the top of F1 had been in doubt since the FIA last week approved the sale of its commercial rights to Liberty Media, though Carey praised the work done by his predecessor over the past 40 years.
"I would like to recognize and thank Bernie for his leadership over the decades," Carey continued.
"The sport is what it is today because of him and the talented team of executives he has led, and he will always be part of the F1 family.
"Bernie's role as chairman emeritus befits his tremendous contribution to the sport and I am grateful for his continued insight and guidance as we build F1 for long-term success and the enjoyment of all those involved."
In a statement released later Monday, Liberty Media confirmed Ross Brawn -- former technical director of the world championship-winning Ferrari and BrawnGP teams
-- will take up the newly-created role of managing director of motorsports immediately.
Former ESPN executive Sean Bratches was appointed managing director of commercial operations
"It's fantastic to be returning to the world of Formula 1," the 62-year-old Brawn said.
"I've enjoyed consulting with Liberty Media these last few months and I'm looking forward to working with Chase, Sean 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."
Retired F1 world champion Nico Rosberg acknowledged news of the takeover.
"Bernie, mega job! But a change has been overdue. Mr. Carey, all the best in making our sport awesome again," he tweeted.