The 21-year-old has signed a four-year contract and joins the Saints for a reported club-record fee of £12million.
Southampton manager Nigel Adkins said: “A lot of hard work has gone in from the football club with a lot of negotiations behind the scenes to get this deal done.
“Great credit to everyone because we have a young, exciting talent joining us who is one of the best around.
“The chairman has gone and backed this deal big-time with the financial outlay, and what we have got is one of the most exciting prospects in world football coming to St Mary’s.
“There is a lot of ambition here and we are all delighted that Gaston is going to come and join us.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.