The Kenyan midfielder has completed a record-breaking switch to St Mary's after two years in Scotland.
The 22-year-old was expected to make a move to England sooner rather than later, with the Premier League's top clubs having been tracking him for some time.
Southampton are the ones to have pieced together an enticing transfer package and Wanyama will start the 2013/14 campaign on the south coast.
He will, however, be forever grateful to Celtic for plucking him from obscurity in 2011 and offering him a stage on which to shine.
Wanyama told Sky Sports News: "It has been hard. Celtic have been good to me and the fans have been great. To be honest it was hard leaving them, but I wish them all the best.
"I had a good time with them. I want to thank them for the time I was there and hopefully one day we will be back.
"I think Celtic have played a big part in my improvement and I want to thank the manager and the players. It was really good and I enjoyed it."
On his move to Southampton, he added: "I'm excited. It's a new challenge and I'm looking forward to it.
"I need to go and work hard and try to get in the team. We will see what happens from there."