The former England boss has signed an 18-month contract, which includes a break clause at the end of the season if the Albion are relegated.
The 66-year-old will take training on Thursday ahead of the Premier League game against Aston Villa on Sunday evening.
West Brom sporting and technical Director Luke Dowling said on the West Brom website: “In Sam we have a man who has a proven Premier League pedigree with a track record of improving every club he has managed.
“We believe and, more importantly, Sam believes we have a group of players that have the quality needed to give the club its best chance of Premier League survival.”
The former England manager will be joined by his long-time assistant, Sammy Lee.
Allardyce has now taken the reins at a record eight Premier League clubs, including Bolton Wanderers, West Ham United, Sunderland, Crystal Palace and in his last role, Everton.