The £12.5m fee is the largest amount involving a Scottish club, beating the £12 million Rangers paid Chelsea for Norway forward Tore Andre Flo in 2000.
Wanyama, who was the Scottish Premier League's Young Player of the Year last season having made 49 appearances and scored nine goals, left Celtic's pre-season training camp in Germany to travel to London to complete the deal.
"It feels great and I am happy to be here," Wanyama told the south-coast club's website after signing his contract at St Mary's. "There were other options, but Southampton is a club with ambitions so I chose to come here."
The Kenyan FA issued a statement congratulating Wanyama for "making history by signing for Southampton".
"As a federation, we are extremely thrilled with this move by Victor. He has always honoured his call-up to the Harambee Stars and every Kenyan should be proud of this move," FKF president Sam Nyamweya told the FA website.
Wanyama has been at Celtic for two years - winning the SPL title twice and last season's Scottish Cup - after joining from Belgian League side Beerschot for £900,000.
Saints' interest in him was confirmed last week manager Mauricio Pochettino who said on Thursday: "I'm very pleased to have secured the signing of Victor because we're a big admirer of his talents and he'll fit in well to the team 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," Pochettino added on the Southampton website.