The 27-year-old right-back, who was born in Switzerland but represents Austria, told Celtic's website: “I’m really, really looking forward to it. I know about the stadium, the historical Celtic Park, and I hope that I can win trophies here and have a very successful season.
“It’s a massive club with a big history and when you see the stadium from the outside and the players there who have already worn the jersey - they are big names.”
Bauer began his senior career with hometown side FC Winterthur, playing for the club's second team before transferring to Grasshoppers.
He played more than 100 games for the Zurich side before joining Rubin Kazan in Russia in 2016. After one-and-a-half seasons he joined Stoke City, making 26 appearances to date.
Bauer was linked with Celtic nearly 12 months ago, with reports the Hoops had enquired about his availability.
He added: “I love being here and having the target of being first as I like that pressure. There are players here who have already won titles, and it’s a big opportunity for me to learn from them and grow as a player as I hope to be part of a successful team.”