The quarterback moves to the NFC West side in exchange for the Cardinals' sixth-round draft pick and a conditional pick in 2014.
The 33-year-old told reporters: "I was presented with a contract [at Oakland] and I was advised not to sign that contract with no security, no guarantees.
"My agent told me that he would never have me sign that contract. That opportunity led me here to coach [Bruce] Arians.
"I've only got a couple shots left. I've been in this league for a long time. It's nothing personal, it's not statistical, it's about trying to win a championship."