The 27-year-old, who is Tony Pulis' first signing of the transfer window, has agreed a four-and-a-half-year contract at The Hawthorns.
"In Jake we have brought in a very, very good player," Pulis told the club's official website.
"I watched him a lot when he was at Tottenham and thought he would go on to establish himself as a top-six player.
"Maybe he has just drifted away a little from that – although having said that two promotions and a cup final with Hull should not be forgotten. But I believe this lad is a very, very good player and I'm delighted we've got him.
"He is a fantastic character and as a player is good enough on the ball but also possesses fantastic energy. He's a good age at 27 and I believe his next three or four years will be his best."
Livermore made 58 appearances for Tottenham before joining Hull in 2013, initially on a loan deal.
Livermore was provisionally suspended by the Football Association and the club in May 2015 after testing positive for cocaine, admitting he had turned to the drug out of grief following the death of his baby son.
The FA confirmed in September that year that they would not extend the ban given the "unique nature of the circumstances". Hull also lifted their sanction.
Livermore has been ever-present in the Premier League this season, scoring one goal in the 3-3 draw with Crystal Palace in December.