The 27-year-old has agreed a four-and-a-half-year deal to move to The Hawthorns after three-and-a-half seasons at Hull, whom he helped gain promotion to the Premier League in 2015/16.
The former Tottenham Hotspur midfielder has made 128 top-flight career appearances and could make his West Brom debut at home to Sunderland on Saturday should he be registered in time.
He is the Baggies’ first January signing, following the loan departures of Callum McManaman, Craig Gardner, Tyler Roberts and Andre Wright.
"Craig Gardner leaving left us short of a certain type of midfield player," West Brom's head coach Tony Pulis told wba.co.uk. "And in Jake we have brought in a very, very good player."