The Australian international departed Parkhead at the end of last season following nine successful seasons at the club which included winning six Scottish Premiership titles, five Scottish Cups and five League Cups.
Rogic has joined the English Championship side on a one-year deal, with the option of a further year, subject to international clearance.
The 29-year-old said: “I heard about the club’s interest in me about a week ago, I spoke with the manager, who seems like a really good guy, and I spoke with my agent and here we are.
“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 and 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 and the boys are looking to change that as quickly as possible.
“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 and the boys are looking to change that as quickly as possible.”
West Brom boss Steve Bruce expressed delight at the signing of a "serial winner". His Baggies side are currently 16th in the Championship having won just one of their opening eight fixtures.
“Tom is a quality player who has played nearly 300 games for Celtic, including a significant number of games just last season," he said.
“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. I’m delighted to have him with us.”