Bruce has been handed the reins at The Hawthorns after Valerian Ismael was sacked as manager earlier this week.
The club moved swiftly to appoint the former Newcastle boss, who left his post at St James' Park earlier this season shortly after the club's Saudi takeover.
Speaking about his new challenge, Bruce said: "I am delighted to have the opportunity to manage a club that has such great history and tradition. It is a club I obviously know well from my time in the Midlands, and I am already relishing the challenge of taking it forward.
"I did not envisage I would return to management this quickly, but once I got the phone call from Ron, I knew I could not resist the challenge of getting this club back to where they want to be.
"I am coming in with one aim and that is to get Albion to the Premier League."
Bruce left Newcastle 13 days after the Saudi-led takeover, with his side winless and in the Premier League relegation zone, and eventually replaced by Eddie Howe.
The Baggies have become the third Midlands club Bruce has managed after spells at Birmingham and Aston Villa.
Ismael departed just seven months into a four-year deal.
Saturday's 2-0 defeat at Millwall left them sixth in the Sky Bet Championship, only in the play-off spots on goal difference and 13 points behind leaders Fulham.
They have won just three of their last 13 games having failed to score in eight of them.
During a day of upheaval the Baggies also underwent a boardroom reshuffle with former Chelsea chief executive Ron Gourlay becoming their new CEO.
The Scotsman, who has also held senior roles at Manchester United and Reading, had been a consultant to the board since July.