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Rumours had swirled for weeks that Stiles would be shown the door after reported run-ins with fellow coaches and key Queensland Rugby Union administrators.
He guided the Reds to just four wins in his first season at the helm.
Chief executive Richard Barker said the QRU decided it was time for a change in culture, discipline and standards.
"We feel strongly that Brad Thorn is the right person to lead this change and that his appointment as head coach is the necessary catalyst for that change," Barker said in a statement.
"Brad has a proven track record of success as both a player and a coach.
"He is without peer when it comes to the culture and professionalism required to be successful at the highest level of our sport and he is enthusiastic about moving the Reds forward and creating a winning culture at Ballymore once again.
Former Melbourne Rebels head coach Tony McGahan has been appointed as Thorn's senior assistant coach.