The 27-year old Houston Dynamo defender has been in talks with the Potters for months now with all terms agreed besides a UK working visa being permitted.
But Stoke have confirmed that USA international Cameron, who had a hearing in Manchester on Wednesday, has received his permit and will now be free to join the Premier League club.
"We are delighted that the appeals panel have approved the work permit and we are now in a position to conclude the transfer," Stoke chief executive Tony Scholes told the club's official website.
"It's been a difficult period between agreeing the transfer deal and the hearing, most difficult for Geoff in particular because his life has been on hold.
"Thankfully though, we have now progressed to a point where Geoff can focus on the start to his career at the Britannia Stadium."