The 32-year-old defender missed the end of last season, including the team's victory in the Europa League final, with an ankle injury.
"I am fit and well," Terry told the club's official website. "I had the injury on my ankle at the end of last season but I came back a week early to get some extra fitness under my belt, and I think that has served me well so far in training.
"It is a big pre-season for everyone and everyone wants to be in the team at the start of the season, and that is what we are aiming for."
Chelsea continue their tour on Thursday when they face the Indonesia All-Stars in Jakarta.