Tounekti, who has signed a five-year deal, revealed other clubs were interested before he completed his move in the final moments of a “hectic” final day of the summer transfer window.
Celtic’s failure to reach the Champions League was no deterrent to Tounekti, who was delighted to make “a nice start” at Rugby Park.
He gave Kilmarnock a tough time down Celtic’s left, but stressed his ability to play on the opposite flank.
“My strongest position is on the left, but I have also played some games on the right so I can play there if the manager wants me to play there,” he said.
“I feel like it is only the beginning. I have so much more to show, so hopefully I’ll bring more out throughout the season.”