After overcoming an apparent impasse in discussions, the highly-rated 22-year-old has put pen to paper on a four-year deal at St Mary's.
Press Association Sport understands Southampton have broken their club transfer record to complete the signing, beating the £12million they spent on Bologna's Gaston Ramirez last summer.
Wanyama's move therefore dwarfs the £9.5million Spartak Moscow paid Celtic for Aiden McGeady three years ago and sees it become the largest fee ever paid in Scottish football, breaking Rangers' long-standing record £12million outlay for Tore Andre Flo.
Until recently it had looked like a move to the south coast had collapsed over personal terms, leading to suggestions of issues with his representatives.
However, manager Mauricio Pochettino last week had not given up on the deal and Wanyama now becomes Saints' second signing of the summer, following the £8.5million purchase of Lyon's Dejan Lovren.
"It feels great and I am happy to be here," Wanyama told the club's official website, www.saintsfc.co.uk.
"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.
"Southampton is a good club and it has good players, so I just want to train hard and work hard to be a part of the starting XI. We'll see where that will take me.
"I'm very grateful to be here and I'm looking forward to playing in the Premier League.
Source: PA
Source: PA