Todt already manages Formula 1 drivers Felipe Massa, Jules Bianchi and Pastor Maldonado, and is confident Calado can join them.
"Through my role at the ART Grand Prix team for whom James is currently in his second year racing in GP2, I have been strongly impressed by his talent, attitude and level of commitment since his very successful GP3 campaign," said Todt.
"I hope that James will fight for the GP2 title and prove that he deserves to enter the F1 elite."
Calado's career so far has been guided by the Racing Steps Foundation organisation.
The 23-year-old Briton has driven for the Todt co-owned ART team since GP3 in 2011.
He finished runner-up to team-mate Valtteri Bottas that year and was a race-winner in his rookie GP2 campaign last season.
Calado stayed in GP2 for 2013 and began the year among the title favourites, although after four races he is fifth in the standings.