The penalty means they have dropped to 20th place, six points above third-from-bottom Oxford United with two games left.
A compliance report to the independent Club Financial Review Panel (CFRP) said West Brom had exceeded the Upper Loss Threshold of 39 million pounds ($53 million) over the three-year period ending in the 2024/25 season.
West Brom denied the allegations.
"Following a hearing on 22 and 23 April and having considered the Compliance Report in full alongside the Club's responses, the CFRP determined that the Club's losses did exceed the Upper Loss Threshold and imposed a two-point deduction, effective immediately," a statement read.
West Brom have 14 days to appeal after receipt of the full written reasons. If an appeal is lodged, it will be heard within 28 days of submission.
A nine-match unbeaten run lifted the Midlands club out of danger, and a 3-0 win at home to Watford last week had apparently taken them out of reach of Oxford before the deduction.
West Brom host second-placed Ipswich Town on Saturday before ending the season against bottom club Sheffield Wednesday.