Bruce had been out of a job since he left Newcastle in October after mutual consent, two weeks after a Saudi Arabian-backed consortium took over the Premier League club.
The 61-year-old will replace Valerien Ismael at West Brom after the Frenchman was fired on Wednesday following a series of poor results.
The club, owned by Chinese businessman Guochuan Lai, also announced the appointment of Ron Gourlay as the chief executive officer on Wednesday.
"Steve is a highly-respected and experienced manager who has an impressive record of earning promotion to the Premier League," Gourlay said in a statement.
"His excellent man-management skills, tactical nous, and ability to hit the ground running were among the many reasons we decided he was the man to take us forward."
West Brom are sixth in the Championship on 45 points after 29 matches, eight points adrift of the second automatic promotion spot.