Adebayor, 27, notoriously ran the length of the pitch when he scored against Arsenal for parent club Manchester City in 2009.
"What happened two years ago was an accident and I do apologise to all the fans of Arsenal," he said. "Sometimes the emotions, we cannot control them, we are all human beings.
"I regret what I have done and I say sorry to everyone but at the end of the day sorry doesn't change anything. For me, it's over."
"But believe me, if I have a chance to score - trust me, I will score - but as for the celebration, never in my life will I do something like that again."
The Togo striker has begun life with Spurs well, scoring three Premier League goals.