"This is a great signing for the club," manager Tony Pulis told Albion's official website on Saturday.
"Jonny brings a lot of experience and will be a big player for us. He's a player I've been watching for some time."
The fee was undisclosed but media reports put it at eight million pounds.
Northern Ireland international Evans, 27, made his United debut in 2007 and played almost 200 games for the club, picking up three Premier League winners' medals.
United hoped the one-club man would develop into a suitable replacement for long-time defensive stalwarts Rio Ferdinand and Nemanja Vidic, who both left in 2014, but he struggled with injuries last season and his form suffered.
West Brom are 14th in the Premier League with four points from their opening four fixtures.
(Reporting by Tom Hayward and Ed Osmond, editing by Tony Jimenez)
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