Woodgate played down his own role in Crouch's transfer following the 30-year-old's claims he worked tirelessly to convince him to move to the Britannia.
"No, 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 believes Crouch will have no trouble slotting into manager Tony Pulis' set-up at Stoke.
He also told The Sentinel: "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."