Sturridge, 28, has scored 63 goals in 133 appearances for Liverpool after joining from Chelsea in January 2013.
He has netted three goals in 14 games for the Merysiders this season and will reinforce West Brom manager Alan Pardew's attacking options as his side battle against relegation.
West Brom are second-bottom of the league with 20 points from 24 games, three points outside the safety zone.
(Writing by Ken Ferris; Editing by Pritha Sarkar)
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