Crouch moved to the Potters last night for a record £10 million fee.
"Woody was on the phone every hour trying to persuade me to come here," Crouch told the club's website.
"He only had great things to say about the Club and that was a major factor in me coming here. He spoke in glowing terms about the Club and the manager.
"I'm looking forward to linking up with him again and a number of other players who have been team-mates at other clubs including Wilson of course."
Crouch is excited at the prospect of a new challenge in an illustrious career which has seen him score goals at the highest level with England and a number of top clubs.
"The future is bright for Stoke," he added. "There are a lot of good players here, it has been a stable Premier League club for a few years now, it has excellent backing from the Chairman and it's top class supporters, so it's a great time to be part of the Club.
"As you can see from the other signings which have been made recently, the Club is really moving in the right direction and looking to do big things now."