Kenya international Wanyama leaves the SPL champions after two seasons in which he made a big impression and won two titles.
The 22-year-old, who had been linked with other Premier League teams, scored 10 goals in his 61 league outings for Celtic, who spent £900,000 to sign him from Belgian side Beerschot.
"It feels great and I am happy to be here, 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," said Wanyama, who was the SPL Young Player of the Year for 2012-13.
"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.
"I've seen that the stadium is great and the dressing room is looking good, and I know some of the players. I hope they will help me and I think I will get along with the others, so it will be good.
"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."
Saints boss Mauricio Pochettino said: "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."