Rodriguez has joined the Baggies for an initial £12m, with the deal potentially rising to £15m.
The Hawthorns side chose a novel way to announce his arrival – responding to a tweet from a fan asking if they had signed anyone yet, Albion replied with a four-second clip of Rodriguez saying “yes we have”.
The 27-year-old struggled with injuries after joining the Saints from boyhood club Burnley in 2012 and failed to secure a regular first-team place under former managers Ronald Koeman and Claude Puel.
He scored 35 goals in 126 appearances for Southampton, who are now managed by Mauricio Pellegrino, after spending five years at St Mary’s and becomes Tony Pulis’ first signing of the summer transfer window after West Brom had tried and failed to recruit him twice in the past.
“After one or two ‘near misses’ I’m absolutely buzzing to be here,” Rodriguez told the club’s website.
“The most important thing for any player is to be wanted – and Tony Pulis and Albion have made it clear just how much they have wanted me to join. That’s fantastic for any footballer to hear.
“I’m genuinely delighted to be joining a club of Albion’s stature. The team is full of top players and it’s pretty clear that they are also a great set of lads.”