The 56-year-old former Stoke City and Crystal Palace manager replaces Alan Irvine, who was sacked on Monday after a run of seven defeats in nine matches that left the club just a point above the relegation zone.
“I’m absolutely delighted to accept the job and I do so with a simple but important message for the Albion fans and everyone at the club,” the Welshman said in a statement on the club website.
“Every successful club is built on unity and that is what I shall strive to help bring to Albion. We need everyone together from top to bottom — the supporters, all the staff, the players, everyone who has an interest in the club’s welfare.
“With that, we can go forward together and hopefully take this club up the Premier League.”
Pulis was named the Premier League’s Manager of the Year for steering Palace away from relegation last season, but he left the club on the eve of the current campaign after falling out with chairman Steve Parish.
He is due to watch West Brom’s away game at West Ham United later on Thursday from the stands, with assistant head coach Rob Kelly taking charge of the first team.
His first game in charge will be Saturday’s FA Cup third-round tie at home to fifth-tier Gateshead.
West Brom reportedly held talks with Pulis and former Tottenham Hotspur manager Tim Sherwood, but Pulis’s record of having never been relegated as a manager gave him the edge.
“We are delighted to secure a man of Tony’s calibre and proven ability,” West Brom technical director Terry Burton said.
“He made it clear that this position excited him and that he was eager to get back into the business of winning Premier League points — and there are few who know how to do it better.”
Irvine, 56, was the second Premier League manager to be sacked this season following Neil Warnock’s dismissal by Palace last Saturday.
Pulis made his name during two spells at Stoke, guiding the club to promotion from the Championship in 2008.
He turned Stoke into an established Premier League side with a reputation for rugged, uncompromising football and guided them to five consecutive top-14 finishes before stepping down in 2013.
Palace were six points from safety at the foot of the table when he took over in November 2013, but he engineered a vast improvement in their performances that saw them finish the season in 11th place.
However, despite receiving many end-of-season plaudits, a disagreement with the Palace hierarchy over the club’s recruitment strategy saw him leave Selhurst Park by “mutual consent” in August.