No fee was given but media reports put the deal at eight million pounds ($12.51 million).
West Brom manager Tony Pulis told the club website (www.wba.co.uk) that the 26-year-old, who started his career at Manchester United, came with glowing references from Hull boss Steve Bruce.
"James did very well for Hull City. I've had a good chat with him and he's the type of player I like," said Pulis.
"He's young, a strong character, a good defender, he has good feet and he has the Manchester United stamp all over him, just like (Stoke City's) Ryan Shawcross and (West Brom's) Darren Fletcher.
"Steve especially gave him a great mention and there is no better accolade than Steve Bruce giving a defender a good drum roll," he added.
Pulis said West Brom, who finished 13th last season, were looking to bring in more players.
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
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