The 22-year-old has reportedly cost the Premier League club £12 million, and becomes Mauricio Pochettino's second signing of the close-season following the acquisition of Dejan Lovren.
"It feels great and I am happy to be here," Wanyama told the club's official site.
"Finally it has happened and we've come to the end [of negotiations], so I am delighted. There were other options, but Southampton is a club with ambitions so I chose to came here.
"I am happy to be a part of Southampton's squad. It means a lot because because it has been my dream to play in the Premier League and now I am here."
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Pochettino was delighted to finally complete the deal, adding: "I am very pleased to have secured the signing of Victor because we are a big admirer of his talents and he will fit in well to the team here at Southampton.
"I want to stress that the deal could have been done sooner, but this shows that we do business on our terms. The most important thing that ourselves, Celtic and the player are all happy with the way it has all gone.
"The fact that a lot of top European clubs were also keen to sign him shows what an attractive prospect Southampton Football Club is to a player who had his pick of the teams in England and abroad.
"I've watched him perform at the top level in the Champions League, and I believe that he will be a valuable addition to our Premier League squad for the season ahead."
Wanyama has spent the last two campaigns in the Scottish Premier League after joining Neil Lennon's side from Belgian club Beerschot AC for £900,000 in 2011.
He won two successive titles during his time in Glasgow, and played an integral role in helping the Bhoys reach the last 16 of the Champions league, scoring the opening goal in their memorable 2-1 win over Barcelona.