Crouch, who arrived at the Britannia Stadium from Tottenham on transfer deadline day, was left out of the most recent England squad by Fabio Capello.
Woodgate told The Sentinel: "He's only been left out of one squad, so it's not about what happens to him in the future, but what happens to him now. He'll probably be in the next squad."
Woodgate played down his own role in Crouch's transfer to the Britannia Stadium.
"I just spoke to him and said how good it was here and that he would be welcome," said Woodgate.
"Peter's a top player - and you want good players to improve your squad. He can only enhance us.
"You're getting an England international whose played at the top level and in the Champions League.
"His international goalscoring (22 in 42 appearances) speaks for itself. And he's played for top teams throughout his career.
"Everybody knows he's top notch in the air, but he's also great on the floor and a good hold-up player. He's a target man with great ability."
Woodgate is also sure that Crouch will fit in at Stoke.
He added: "Crouchy's also a genuinely nice lad. There's no airs or graces. There isn't a big-time bone in his body.
"He'll fit right in here because there is a really good team spirit."