Alan Irvine was sacked by the club after a run of seven defeats in nine Premier League games left them 16th in the table, just a point above the relegation zone.
Pulis was understood to be concerned with the management structure at the club, where former Wimbledon boss Terry Burton is technical director and Richard Garlick the director of football administration.
But after being reassured he would have a key say over future signings, the Welshman appears set to take the role.
The 56-year-old will now be charged with retaining the Baggies’ top-flight status but will not be in place for the New Year’s Day game with West Ham at Upton Park.
Pulis could take charge of West Brom for Saturday’s FA Cup third round game with Gateshead at The Hawthorns, though, where he would become Albion’s fourth head coach in just over a year since Steve Clarke was sacked in December 2013.
Pulis was initially thought to have been in the running for the Newcastle job if, as expected, Alan Pardew leaves to become Crystal Palace boss, but sources understand Pulis was never under consideration for the St James’ Park hotseat.