Smith told the club's official website: "It's just a dream come true. Everything that I wanted to happen fell in place. Yesterday, when my name got called, I was very happy and my family was happy and I'm just happy to be an Eagle.
"Going into [the Draft], I had an idea when I was going to get drafted. It was a surprise to me when [the Eagles] called me, but I was very happy when they called me and told me that they were going to be drafting me.
"I just want to be a part of something special, and I know they have something special in this organisation. I just want to be a part of it."
Smith recorded 42 tackles and 14.5 sacks for the Cardinals in the 2013 season.