The Senegal international joined the Blues in a €40m deal last summer after eight seasons at Napoli.
He had refused to sign a contract extension with the Azzurri before his move to Stamford Bridge.
“I knew that after eight years, my time at Napoli was over,” he told France media Carré, as quoted by TuttoNapoli and Il Corriere Dello Sport.
“When one of the best clubs in the world calls, you can’t wait. I did all I could to join Chelsea. I will forever be grateful to Napoli and Naples. My children were born there and it’s the place where I’ve become a man and a footballer, but it was time to change.”
Koulibaly was a regular starter under Thomas Tuchel, but things seem to have changed after the German tactician was sacked and replaced by Potter.
Koulibaly hasn’t featured in any of the two games played by the Blues under their new coach.
Despite that, KK has no regrets about his move to Stamford Bridge.
“I have settled in well, just like my family,” he said.
“I arrived at the right time, along with players who have won many trophies. It’s up to me to prove that the team can always count on me. For now, I am really happy and I hope to continue.”
The 31-year-old played 317 games with Napoli, scoring 14 goals. He won one Coppa Italia and one Italian Supercup during his eight-year spell at the Stadio Maradona. This past January, he captained his country Senegal to win their first international trophy lifting the African Cup Of Nations in Cameroon.