The 22-year old Kenyan midfielder has joined the Saints on a four-year deal for a fee believed to be around the £12.5million mark, making it a club record.
Wanyama, who starred for Celtic after arriving from Belgian club Beerschot in 2010, was thrilled to have made the move to the Premier League.
"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.
"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 it has been my dream to play in the Premier League and now I am here."