The 30-year-old former Australia international joins the Super League club after being released by Catalans Dragons in October.
Salford CEO Ian Blease said: "Todd will be a vital part of our jigsaw and is a real statement of our intent. He is a world-class player and match-winner.
"We are delighted to get his signature and are greatly looking forward to his arrival for the start of season."
Carney is a previous winner of of the southern hemisphere competition's highest individual honour, the Dally M Medal, and was the international player of the year in 2010.
Salford Red Devils have signed half-back Todd Carney for the 2017 season.