Wanyama agreed a four-year contract with the Premier League club after lengthy negotiations, and his arrival is believed to have broken the previous record fee Saints paid for Bologna's Gaston Ramirez last year.
The 22-year-old's move surpasses the £9.5m Spartak Moscow paid Celtic for Aiden McGeady three years ago, making Wanyama the most expensive export from Scottish football.
His deal is also the largest fee ever involved in a Scottish football transfer, breaking Rangers' long-standing record £12m outlay for Tore Andre Flo.
Wanyama had been with Celtic for two years, having arrived as a relative unknown from Belgian side Beerschot. Choosing the number 67 jersey in appreciation of the Hoops' European Cup triumph, he quickly became a fans' favourite. Wanyama shone for the Glasgow giants and his UEFA Champions League performances saw his stock rise, persuading Southampton manager Maurico Pochettino to make his record out-lay.
"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," Pochettino said.
"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 is 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."