The highly-rated 22-year-old was finally given the green light to make the switch from MLS side FC Dallas to the Britannia Stadium on Thursday evening after the Potters secured a work permit in an appeal hearing in London which was attended by boss Tony Pulis.
And, having obtained all of the necessary international clearances, both Shea and Pulis are looking forward to the player testing his abilities in the Premier League.
"It's fantastic news that we have been able to push through the deal," said Pulis on the club's website. "Brek is a very, very exciting player, and one who we firmly believe could go on to become an outstanding player for this Football Club.
"He has terrific pace, a very good left foot and is capable of scoring goals. He has all the tools needed to be a success here."
Shea added: "It's been up and down, trying to figure out what's going on, but I'm here now and ready to go. It's one of the best Leagues in the world, and I'm excited to be here and hopefully I can contribute."