The deadline-day deal, which is believed to be worth around £12m, will see the 19-year-old defender stay on loan with the Ligue 1 side for the rest of the season before moving to Stamford Bridge in the summer.
"I live with great joy and happiness," Zouma told reporters. "It suits many people. Everyone is happy with this, so it is satisfactory.
"This is especially because this is my first transfer, and it makes me really happy. I saw it with great joy and happiness."
Zouma joined Saint-Etienne as a youth player in 2009.