Gardos has joined the Premier League outfit from Romanian champions Steaua Bucharest for an undisclosed fee, reported to be in the region of £6 million.
The 25-year-old claimed finalising his move was a landmark day in his career.
"This is one of the happiest days of my life," Gardos told Southampton's official website.
"It's the biggest step of my career so far. Coming to the Premier League is a very big occasion for me, and Southampton was a team that had a really good last season so this wasn't really a hard decision.
"I've had a very good first impression of the club. I've always said that coming to [the] Premier league would be a dream come true."
Gardos has won 12 caps for Romania and is the club's seventh close-season signing after forward Shane Long moved from Hull City earlier on Thursday.
Southampton manager Ronald Koeman is hoping Gardos can fill the void left by Dejan Lovren, who moved to Liverpool last month.
Koeman said: "I am very happy to have Florin here.
"He's still a young player so he can develop himself a lot more, and that's part of the ambition of Southampton.
"After [Dejan] Lovren left the club, we paid a lot of attention to Florin. For now and for the future, we have a very good central defender."
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