The 33-year-old Warner, who played for the New York Giants last season, has a one-year contract with Arizona.
The Cardinals, who started Josh McCown at quarterback most of last season, announced Warner's signing Sunday and plan a news conference Tuesday to introduce him.
"Even though this is a one-year deal, I really don't want to go anywhere else and would like nothing more than to end my career by helping the Cardinals win a championship," Warner said.
Warner, who led the St. Louis Rams to the Super Bowl championship in 2000, started seven games last season for the Giants.
"Bringing Kurt Warner on board this fast-moving train is very, very exciting," Coach Dennis Green said. "He's proven he's one of the best competitors in the National Football League, regardless of position, and is one of the bravest quarterbacks ever to play the position."