Smith, 26, has agreed a five-year contract and trained with his new team-mates on Friday.
Smith said after signing: "The biggest thing for me is to get back playing regularly and to come to a place like this and to play football.
"Everyone already knows about how passionate Newcastle is, what their fans want to see, and how much they want success.
"It's nice to come to a place where a manager is trying to build a team and build a squad to develop and push on further and he wanted me to be part of that. When someone says that to you its always nice."
Smith could make his Newcastle debut alongside former Leeds team-mate Mark Viduka in a pre-season friendly against Sampdoria on Sunday.