Wanyama, who revealed he had been won over by the south-coast clubâ€™s dogged determination to land him, had already said his farewells to his Celtic team-mates on their current German tour before jetting off to seal the bumper deal.
"I am happy to be part of Southamptonâ€™s squad," said the powerful midfielder. "It means a lot because it has been my dream to play in the Premier League and now I am here.
"Finally it has happened and weâ€™ve come to the end of negotiations, so I am delighted. There were many clubs that inquired about my services over the past season, but itâ€™s Southampton who kept on trying to acquire my services, and that trust is very important.
"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. Weâ€™ll see where that will take me. Iâ€™m very grateful to be here.
"Iâ€™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."