Austin has twice been denied a work permit to complete a move to Stoke but he will now be allowed to make the switch after appearing in two World Cup qualifiers for Jamaica earlier this month.
The county are no longer ranked as one of the world's top 70 sides but the Potters will be allowed to sign the 22-year-old once they have agreed a fee with his club Portmore United.
"We will make sure the deal is the right deal for our football club," said Pulis. "Rudolph is only a young lad and so if he does well then we will make sure that they (Portmore United) are rewarded."
Austin has attracted the interest of clubs in Brazil and the United States but he should become a Stoke player before the start of the new season and Pulis is excited to get him on board.
"I really like him. He's very quick, has got two good feet and he's good in the air," he added on BBC Radio Stoke.
Meanwhile Pulis has hailed the club's decision to house supporters on all four sides of the Britannia Stadium for their debut campaign in the Premier League.
"I think it's a great idea because we need our fans generating atmosphere all around the ground," he told The Sentinel. "It's a pity they can't be by the tunnel for when the players come out, but you can't have everything.
"It worked a treat in the last few games of last season, particularly in the home win over Bristol City, and it obviously gives us more room as well to get our supporters into the stadium.
"Atmosphere must be a huge weapon for us at home in the Premier League and I've got no doubts those in the South Stand will do us proud.
"It will feel like we've got two Boothen Ends at the Britannia."