The 23-year-old second rower, who shocked the Bulls by asking for a move, will join the French club immediately on a contract running to the end of 2015.
Whitehead, who told Bradford he wanted to join a top-four club, rejected an offer from Salford to become Catalan's second signing in the space of 24 hours, after they snapped up utility forward Benjamin Garcia from Brisbane Broncos.
"It's really good news for the end of the season because Elliott will bring enthusiasm and competition into the squad but also for the future because he is a young quality player," said Dragons coach Laurent Frayssinous.
"Elliott is a Super League rising star. He shares our project and our ambitions."
The Dragons have paid an undisclosed transfer fee for Whitehead, who was under contract with the Bulls until the end of 2016 but will help fill the void created by injuries to back-row forwards Louis Anderson, Oliver Elima and Jason Baitieri.
Catalan chief executive Christophe Jouffret said: "We have many players sidelined long term and we considered the option to sign a short-term player until the end of the season, but the opportunity to sign Elliott on a two-and-a-half-year deal was more interesting for the club.
"The discussions with the Bulls were really longer than those with the player, who give us his agreement when I met him last weekend."
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