Abiteboul was already the chief executive of the Britain-based team, which has yet to score a point in three years, and will now combine both roles.
"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," said Fernandes in a statement.
"He takes over during a season when we have not yet fulfiled 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 One and he is the right person to take us there."
Abiteboul was previously deputy managing director of Renault Sport F1 and spent 11 years with the French car manufacturer. Renault provide the engines for Caterham's cars.