The 24-year-old was named in Roy Hodgson's squad for the forthcoming friendlies against Chile and Germany along with Saints team-mates Adam Lallana and Rickie Lambert.
Rodriguez admitted he was stunned when told the news by Southampton manager Mauricio Pochettino at the club's training ground on Thursday morning.
"Words can't describe it - I'm obviously still shocked," Rodriguez told the Southampton website. "It's a bit surreal.
"It's a dream come true, really. I couldn't believe it when I was told, and I haven't stopped smiling all day.
"It's been important for me to concentrate on my football and improving as a player, and hopefully this will improve me massively.
"I've been focused on my club games and my performances there, so I had to keep my feet on the ground and keep working on that. Now I just can't wait to get among the lads and be a part of it."
Lambert made his England debut in August and will be bidding for his fifth cap against Chile next week, while Lallana has yet to feature although he was on the bench for the clash with Ukraine last year.
"It's unbelievable for the club," Rodriguez added. "It just shows the direction we're going in and the ambition and vision we've got.
"We have so many international players now, so it's a really good place to be and a good thing to be part of.
"It's always nice if you know someone there, but Rickie has said before that the lads make you welcome there. It's something to look forward to and I'm just excited to get started.
"The most important thing at the moment is the game on Saturday, so we've got to keep our heads on for that and keep concentrating - but this is a dream come true, so you obviously can't help thinking about that.
"It's a really good feeling, but I still feel I've got a lot to improve on in my game - and that's what I want to do.
"I'll keep my head down, work hard and I'll keep taking on these challenges."