Pardew, 56, who has been out of work since he was sacked by Crystal Palace in December 2016, has agreed a two-and-a-half-year contract with West Brom, one of the oldest clubs in England.
"I'm thrilled with the opportunity Albion have provided and looking forward to getting to work with what I consider to be a talented group of players," Pardew told the club's official website.
"The immediate challenge will be to get the results we need to pull ourselves up the table. But I'm aware that while I'm joining one of the great, traditional clubs of English football, it is one determined to go forward in the Premier League."
He added: "It's an exciting opportunity to play a part in that ambition."
John Williams, the West Brom chairman, said the club's board had reached a unanimous decision to emply Pardew. "Alan brings the experience of more than 300 Premier League games and the kind of dynamic leadership from which our club can benefit," he said.
"We were impressed with what he had to say and what he has to offer and we are looking forward to an exciting new era under his charge."
Pardew, the Premier League manager of the year in 2012, has a history of touchline meltdowns.
In 2014, when he was the manager at Newcastle United, he was fined and given a formal warning for headbutting an opposition player. During his time at the helm of West Ham, he was involved in a furious row with the Arsenal boss Arsene Wenger.
Pulis was sacked on 20 November following a 4-0 defeat at home to Chelsea on 18 November.
Under Pulis, West Brom finished 14th in the 2015-16 season and came 10th last season. However they failed to win any of their final nine matches.
That slump tainted the start of the 2017-2018 season. West Brom have only two wins from 14 Premier League matches this season and lie in 16th place with 12 points.
Pardew faces his former club Crystal Palace in his first match in charge on Saturday. Tough fixtures loom later in December against Liverpool and Manchester United.