The safety, who was a free agent after failing to reach a new agreement with the San Francisco 49ers, signed a five-year contract worth $41.25m (£27.2m).
The 28-year-old told The AP: "I was very thankful I didn't get the franchise tag again, just so I could see my opportunities out there.
"I think this is the correct fit. I really truly believe that. It was time to go somewhere that really, really wanted me."
Goldson recorded 69 tackles for the 49ers in 2012, as well as a forced fumble and three interceptions.