The 23-year-old United States international striker signed a four-year deal on Tuesday night as he completed his move from AZ Alkmaar for an undisclosed fee.
Altidore told the club's official website, safc.com: "I'm excited.
"Anybody who knows anything about football knows that the Barclays Premier League, when you look at everything as a full package, is the biggest league in the world.
"I'm thrilled to be here and I'm looking forward to getting adjusted as quickly as possible.
"It's a fantastic club, everyone here is so welcoming. I'm really excited about this season - it has everything here, all the combinations to be a big club, so I'm really excited to be a part of it."
He said: "It's great, it's part of taking that next step as a player.
"To be able to play in front of a stadium like that is going to be really exciting - I hope they like what I do on the pitch.
"Everybody, I'm sure, is excited to get the season off to a good start and I'm no different.
"I can't wait to meet the guys, meet the coaching staff and get acclimatised as soon as possible.
"I'm just going to give everything I can to the team, that's the biggest thing, to get the respect of your team-mates and when you do that, I think everything will fall into place.
"I'll just give my all for the club. I really appreciate the club making the investment in me as a player and I want to give that back."