Woodgate won the last of his eight international caps in 2008 but has been given the chance to kickstart his career at the Britannia Stadium.
The 31-year-old former Leeds, Newcastle and Real Madrid defender saw his progress seriously hampered by injury over the last few years and was released by Tottenham at the end of last season.
Bad breaks: Jonathan Woodgate has been unfortunate with injuries
He has since signed a pay-as-you-play 12-month deal with the Potters and could make his debut against Hajduk Split in the Europa League qualifier on Thursday - Stoke's first European tie for 37 years.
And manager Pulis is expecting big things from Woodgate.
He said: 'He's been first class. The way we've structured Jonathan's contract is beneficial to both. If he plays in the team then he'll be on the wages the rest of them are earning, and if he doesn't then he won't.
National service: Defender Woodgate playing against Spain in 2007
'But Jonathan took that gamble, we managed to persuade him to do that, and I think it's fantastic. He's a good player, he's a good lad, and he's really settled in.
'I think he's been pleasantly surprised by the way he's been received and how good the club is in lots of ways.
'Woody's got an opportunity to play regularly - if he does well he could get called up for England again. He just wants to play.'
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