West Brom announced the deal via a video on their Twitter account, in which Rodriguez responded to a fan's concern that the club was yet to make any new signings.
He missed the entirety of the 2014-2015 campaign and has found it hard to get playing time for the Saints since.
A call-up to the England senior squad followed, but an untimely ACL injury ruled him out of contention for the 2014 World Cup finals in Brazil and he has not featured on the worldwide stage since.
Salomon Rondon endured a five-month goalless streak last season, and with little support around him, Pulis has chosen to land Rodriguez in a bid to bring more goals to his Baggies side.
Tony Pulis and Albion have made it clear just how much they have wanted me to join.
"The target is to set our sights as high as possible and be the best that you can be - both as a team and an individual", he said.
Rodriguez, 27, joined Southampton from hometown club, Burnley, back in the summer of 2012 following the Saints' promotion to the Premier League, and he enjoyed a decent first season with nine goals to his name.
"If the England squad opens up for me again as a result, that would be fantastic".
"After one or two "near misses" I'm absolutely buzzing to be here," says Jay, referring to Albion's two previously thwarted attempts to recruit him from the St Mary's Stadium.
"There is a lot more to come from me".
Rodriguez has struggled with injuries in recent seasons but has scored 32 goals in 126 matches over five years with Southampton.