The Saints made the announcement on their official club website, stating that the deal was agreed over a week ago, and "only the finger details of the transfer prevented his signing from being completed." The Uruguayan has signed a four-year deal with the South coast club.
Saints boss Nigel Adkins stated: "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 at the Football Club and we are all delighted that Gastón is going to come and join us."
Ramires is in Uruguay's squad for their next two World Cup qualifiers against Colombia and Ecuador, which will take place in the upcoming International break. Ramirez is expected to make his debut against Arsenal the following week.