The 26-year-old, who is a product of the Brisbane academy, made his debut for the outfit in 2010.
Speaking to the club's website, Warrington head coach Tony Smith said: "We are delighted with the signing of Mitchell. He's played a big part in the Broncos' team this year.
"He's played most of his games off the bench and they are in there fighting for a title as we speak. We need that sort of experience coming into our squad.
"He is a no-nonsense hard-hitting prop forward who is probably best known for his defensive efforts - we need to strengthen in that area as it's probably not been our strongest year defensively."
Dodds has made 72 appearances for the Broncos, scoring three tries.