Livermore, 27, joined Hull initially on loan in August 2013 and moves to the Baggies on a four-and-a-half year deal.
"Jake is a fantastic character and as a player is good enough on the ball but also possesses fantastic energy," said West Brom boss Tony Pulis.
West Brom have also enquired about Watford striker Odion Ighalo, 27.
Read more: Hull sign right-back on loan
Talks are only exploratory at this stage but Ighalo has fallen out of favour at Vicarage Road and is a player long admired by Baggies boss Tony Pulis.
The Nigeria international scored 17 goals in 42 games last season as Watford finished 13th in the top flight and reached the FA Cup semi-final. However, he has managed just two goals in 19 appearances so far this season.
Former Tottenham player Livermore is Pulis' first signing of the January transfer window after the club missed out on Morgan Schneiderlin, who joined Everton from Manchester United.
"I watched him a lot when he was at Tottenham and thought he would go on to establish himself as a top-six player," added Pulis, 59.
"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."
Pulis' side are eighth in the Premier League ahead of a trip to Sunderland on Saturday. Hull sit 18th after beating Bournemouth in a first league win since November and travel to Chelsea on Sunday.
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West Brom have completed the signing of Hull City midfielder Jake Livermore for an undisclosed fee, believed to be £10m.