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Livermore, 27, who on Friday signed a contract for the next four and a half seasons, has become the first reinforcement of the set coached by Tony Pulis in this winter transfer market, reports Efe.
The English midfielder, who began his career in the youth teams of Tottenham, with which he played 58 games, signed for Hull in January 2014 after being loaned out a year earlier.
"In Jake, we have brought in a very, very good player. I watched him a lot when he was at Tottenham and thought he would go on to establish himself as a top-six player," Pulis said in a statement to the West Brom website.