Cole chose a move to Chelsea, where he went on to win the Premier League.
He left in 2006, with financial reasons also touted as a cause for his move at the time.
Cole did win two league titles with Arsenal before his departure, but lifted the biggest prize in club football as a Blue - the Champions League.
"The transition in terms of being in a different group, environment and players was easy because at the time when I first started at Arsenal, we had a core – the Keowns, the Seamans, the Vieiras, the Henrys, the Adams'," Cole told BBC Sport.
"When they started to leave, I felt there were holes in the culture of what it was that brought success. I just felt it was falling apart a bit, or there were gaps missing and they weren't filled.
"So that transition in terms of finding myself in a different culture and the willingness and want to win, I went to Chelsea and I had that."