The defender left Celtic to join the Premier League side for a reported £12.5m transfer fee.
"I believe one day Champions League football is achievable at Southampton. Everything step by step and I believe one day we will be also there," BBC Sport quotes the Kenyan international as saying.
"It was my decision after meeting with the chairman and the manager. I was just happy with the things they were telling me and that's why I chose Southampton. The ambition of the club they had and I was just happy to come and join them.
"It has been a little bit easier to get used to the change, because the teammates here have been really helpful and it has been easy for me to settle in."
Southampton play West Ham United at St Mary's tomorrow afternoon.