Wanyama completed a £12m move from Celtic to St Mary's last week after two successful seasons with the Scottish champions.
The 22-year-old has admitted that it was tough to leave the Glasgow giants, but is relishing the challenge of shining for Mauricio Pochettino's side.
He told reporters: "It was hard leaving them [Celtic], they were good to me but I wish the fans all the best. Hopefully one day we will be back.
"I'm excited, it's a new challenge to play in the Premier League. It means a lot to be the first Kenyan in the Premier League, but I have to work hard to get in the team and then we will see from there."
Wanyama's acquisition took Southampton's summer spending passed the £20m mark, with their other major close-season signing Dejan Lovren joining from Lyon last month.