The club were successful with their appeal at a hearing at Wembley and are hopeful of finalising the transfer before the 11pm deadline.
A Stoke statement said: "The club were successful with their work permit appeal in London this afternoon and now hope to finalise the deal.
"Manager Tony Pulis attended the hearing at Wembley along with other club representatives to present City's case to bring the 22-year-old winger to the Britannia Stadium and were given the green light.
"City hope that the transfer of Shea can now be pushed through before the transfer deadline at 11.00pm this evening."
Shea has already passed a medical with the Potters but the deal was held up as he does qualify for a work permit under current regulations.
Shea was required to have played in 75 per cent of the USA's international games in order to be awarded a permit, but he has only featured in 14 games over the past two seasons.
However, that was largely due to Shea undergoing an operation last August to remove a bone in his right foot, forcing him to miss several internationals, and Stoke have successfully argued mitigating circumstances.
"They're a bunch of good guys & I'm looking forward to getting started here, but I need a Visa first," said Shea.