The 56-year-old Pulis will replace Alan Irvine who was sacked on Monday following a run of seven defeats in nine games.
The BBC reported that Pulis is likely to be confirmed on Thursday and will be in the stands at Upton Park for West Brom's New Year's Day Premier League visit to West Ham United.
Pulis managed Stoke from 2006-13 before joining Palace and he guided the south London club to 11th place in the top flight in his one season in charge.
He quit the job two days before the start of this season amid reports of a falling out with Palace co-chairman Steve Parish.
West Brom are 16th in the 20-team standings, one point above the relegation zone.
(Reporting by Toby Davis; editing by Amlan Chakraborty)
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