Bauer in action for Rubin Kazan
The right-back was signed for an undisclosed fee and becomes the Potters’ first signing of the January transfer window.
Bauer agreed terms and underwent a medical last week and has now completed the formalities of his switch to the bet365 Stadium.
Chief Executive Tony Scholes said: “Moritz is a player we have been trailing for some time and was someone Mark Hughes wanted to bring into the Club.
“Moritz came over to England last week to undergo his medical and discuss terms and we have now been able to conclude his transfer.
“He’s a very highly-regarded player who broke into the Austrian senior side last year and he adds to the defensive resources at our disposal.”
Stoke currently sit 18th in the Premier League and face a daunting trip to Old Trafford next Monday.
They currently boast the worst defensive record in the league, having conceded 47 goals from their opening 22 games.