The highly-regarded 23-year-old, who is part of the Ferrari young driver academy, is currently in his rookie season with Marussia.
Marussia will have Ferrari engines next year, when the rules go through major changes and a new V6 turbocharged unit is introduced.
"It gives us great pleasure to announce that we will go forward into 2014 with Jules as one of our race drivers," team principal John Booth said in a statement at the Korean Grand Prix.
"Jules joined us at very short notice at the end of pre-season testing, with only two days of running under his belt.
"He rose to the challenge of his debut season exceptionally well and since that time has clearly demonstrated his ability and potential."
Bianchi's best result to date is 13th in Malaysia, with Marussia currently 10th of the 11 teams in the constructors' standings despite having so far failed to score a point in Formula One.
Booth said the second driver would be announced later in the year.
Britain's Max Chilton is currently Bianchi's team mate.
(Reporting by Alan Baldwin, editing by Greg Stutchbury)
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