The 27-year-old made the switch between Premier League rivals on Sunday afternoon, setting long-term admirers Albion back around £15m should he hit various incentive-based targets.
Rodriguez was left frustrated by a number of injury issues during his five-year spell on the south coast, reserving his best form for the 2013-14 campaign when netting 15 times.
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 international stage since.
A change of surroundings has previously paid dividends for Jake Livermore, who was himself involved for the Three Lions last season, and Rodriguez hopes to go the same way as his new teammate.
"The team is full of top players and it's pretty clear that they are also a great set of lads," he told Albion's official website. "And you look at what has happened to Jake after he joined, getting back into the England squad. My aim is to keep improving, keep working hard and hopefully help Albion get better.
"If the England squad opens up for me again as a result, that would be fantastic. There is a lot more to come from me. 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.
"I obviously was close up in the two Albion-Southampton games last season and I could see there was a blend of strong players and also flair players. I was impressed and I am buzzing to be joining the group."
Rodriguez scored 32 goals in 126 appearances overall for Southampton upon joining from Burnley in 2012.