The 21-year-old playmaker has signed a four-year contract at St Mary's with the Barclays Premier League club revealing that a verbal agreement was in place last Friday.
A statement on the Saints' official website read: "Saints are pleased to confirm the signing of Uruguayan international Gaston Ramirez from Italian side Bologna."
Saints manager Nigel Adkins added: "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 at the football club and we are all delighted that Gaston is going to come and join us."
And Italian international Borriello joined Genoa, one of his former clubs, from AS Roma for an undisclosed fee.
"Il Grifone has rediscovered one of those strikers who has written his recent history to the sound of goals," Genoa announced on their website.
The 30-year-old forward spent six months on loan at Italian champions Juventus last season, scoring twice in 13 appearances, but failed to impress manager Antonio Conte enough to seal a permanent move.
Borriello's previous spell at Genoa during the 2007-08 season yielded 19 goals in 35 games before he returned to AC Milan, the club where he began his career and that still part-owns him.
His return to Genoa was made possible following the departure of Alberto Gilardino who has joined Bologna on loan.