Gazzaniga agreed a four-year contract with the Saints and is expected to push current first choice keeper Kelvin Davis for the number one jersey next season.
The 20-year-old has enjoyed a rapid rise to prominence after just half a season in goal for League Two club Gillingham.
"I am very happy because signing for a Premier League team is a dream," Gazzaniga told Southampton's website.
"It's mad because I only played a few matches last season - it's a crazy situation.
"The club has a lot of ambition, so I was eager to sign. I can't wait to get started."
Gazzaniga, the son of professional goalkeeper who played in Argentina, Ecuador and Peru, moved to Spain aged 15 to pursue his own career and joined Valencia in 2010.
He was released the following year, but joined Gillingham in time for the start of last season, establishing himself as number one in the second half of the campaign.
Southampton manager Nigel Adkins added: "He is very ambitious, he is young and hungry and wants to do well.
"He was with Valencia the year before last before coming over to England and getting some games under his belt at Gillingham, which is where our recruitment department spotted him.
"He has a good stature about himself, he is a young lad who has an assured confidence about himself."
Gazzaniga becomes Southampton's fourth signing since securing promotion to the Premier League, following the acquisitions of Jay Rodriguez, Steven Davis and Nathaniel Clyne.
Source: AFP
Source: AFP