"#SaintsFC can confirm that @JayRodriguez9 has today completed a move to #WBA," they said.
Although no fee was mentioned, British media said the deal was worth 12 million pounds.
The 27-year-old's career has been disrupted by a series of injuries which saw him miss the whole of the 2014-15 season and struggle to break back into the Southampton first team.
He scored 32 goals in 126 appearances for Southampton, whom he joined for seven million pounds from his home-town club Burnley in 2012.
Rodriguez has one cap for England.
(Reporting by Neil Robinson; Editing by Rex Gowar)
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