The Australia international left Celtic at the end of last season for a "fresh challenge", with the Baggies holding the option of a further 12 months should the midfielder impress at The Hawthorns.
Rogic told the club's website: "I was looking for a change of scenery and a fresh challenge. I didn't just want to rush into anything.
"I think it was important for me to take my time and make sure my next club was the right club.
"I had some time to reflect and I now feel refreshed, re-energised and excited about the future. I'm really looking forward to getting started at Albion.
"I think it's fair to say the team hasn't got the results the performances have warranted so far this season. I know that the manager (Steve Bruce) and the boys are looking to change that as quickly as possible."
Boss Steve Bruce said: "Tom is a quality player who has played nearly 300 games for Celtic, including a significant number of games just last season.
"He has proven to be a quality player, a serial winner and a top professional. He can play in several positions across midfield and I'm confident he will prove to be a great acquisition for the club."