Widely regarded as one of the best players in the Championship, the 28-year-old put pen to paper on a four-year deal at The Hawthorns last week.
Albion beat off competition from a host of clubs to land the former Millwall man – with Burnley and Watford also believed to have been chasing his signature.
Wallace is Albion’s second capture of the summer – with manager Steve Bruce also beating off rival clubs to land John Swift.
And Swift’s arrival helped convince Wallace that the Baggies are serious about winning promotion this year.
“When you look at this club over the last 15 years, certainly in my life-time, they’ve always been at the top of this league, if not the league above,” he said.
“That aligns with where I want to be playing my football.
“I think it’s a huge show of intent to bring Swifty in, who I know.
“That’s a very impressive signing. He’s a top quality player at this level, along the rest of a very talented squad.
“I want to get promoted. I’ve been trying to do that for the last three or four seasons. I feel like I can find that ambition here.
“Hopefully we can reach our goal, which is to have a few bottles of champagne, a little party and promotion at the end of the season.”
Wallace revealed manager Bruce was also key to his move to The Hawthorns.
“When I spoke to him, I felt like I’d play my best football under someone like him,” he added.
“You’re going to get interest. I spoke to a few clubs.
“I just felt it was the right time, at my age, to be really ambitious and to take the next step in my career.
“This club wants to be in the Premier League. The manager has had huge success at this level before.
“Goals and assists are one thing, but I want to finish as high up the table as we can.
“I don’t care to be honest about personal numbers, I just want to play in the Premier League.”