Terry decided this week not to appeal the decision, leaving Chelsea to decide what action of their own to take.
Gary Cahill and Juan Mata have both welcomed the news Terry will remain as captain.
Speaking after Saturday's 4-2 victory at Chelsea, Cahill told Sky Sports 1: "Fantastic, I didn't really expect any other outcome to be honest. He has been captain for many years."
Mata added: "He is a great team-mate and a really good guy."