The 22-year old Kenyan midfielder has joined the Saints on a four-year deal for a fee of £12.5million - a Southampton club record - and leaves Parkhead with the best wishes of the Scottish champions.
"Victor Wanyama this afternoon completed his transfer to English Premier League side, Southampton FC. The move is one which Victor makes following two successful years at Celtic," read the statement on the club's official website on Thursday.
"Since arriving in the summer of 2011, Victor made a big impression on Scottish and European football with his contribution to Celtic's success at home and abroad.
"Now the popular Kenyan has decided to take up a new challenge in England's top flight at Southampton. He leaves Celtic with the best wishes and support of everyone at the Club as our own preparations continue for the new season."