Abiteboul joined Caterham as F1 team CEO in September and will combine that role with his new responsibilities as team boss.
Fernandes confirmed on Tuesday that he will step down as team principal of Caterham before the end of the season in order to focus more on developing the company's road car business.
"I am honoured to take over as team principal, now combining that role with the CEO post I took up in September 2012, and I would like to thank Tony and [Dato'] Kamarudin [Bin Meranun] for the chance to lead this team into the next phase of its growth," said Abiteboul, who is also working at Renault Sport until next year.
"We have big challenges ahead of us but the shareholders are committed and behind us to help us take significant steps forward over the coming years, and one day challenge for the highest honours in F1.
"We have an incredible spirit within the team and that has been created by Tony and Kamarudin. This spirit, allied to a strategic vision that gives us a clear path to success, is what will keep driving us forwards and we all look forward to the day we can make the dreams our shareholders had several years ago come true."
Fernandes has backed Abiteboul to do a great job in his new role.
"Cyril is going to be an excellent team principal. He has extensive experience in F1, he is extremely well respected and he shares our vision for what we want our team to achieve.
"He takes over during a season when we have not yet fulfilled our potential, but at a time when we have everything in place to help us do so. One day we will earn our seat at the top table of Formula 1 and he is the right person to take us there."