The French defender was signed from St Etienne last season but spent the remainder of the campaign on loan at the Ligue 1 side.
Now, however, the 19-year-old has joined up with the Blues for good and is playing a prominent role in pre-season.
Terry, meanwhile, believes Drogba's winning mentality is rubbing off on Zouma, who could be the 33-year-old's long-term successor.
“He’s still the same, a nightmare to play against in training, still physically strong, sharp and hungry as well," the Blues captain told Chelsea TV.
"It’s important Didier is here because he brings that mentality of wanting to win every day and that rubs off on people like Kurt Zouma and the other young players he’s playing against.”
Terry has also given his view on Frank Lampard's move to Manchester City, commenting that it simply does not feel right seeing him play for another club. It is the same, Terry says, with Ashley Cole at Roma.
“It just doesn’t seem right to see them in different shirts. Maybe over time that will ease but it doesn’t seem right.
“We have grown up together and won and lost together at Chelsea. We have done many great things and it was sad to see them go.”
Chelsea will open their Premier League campaign at Burnley, where Terry and Gary Cahill will likely begin another season-long partnership.
Last term, the duo were responsible for a defensive record that kept the most clean sheets in the top flight and conceded the least goals. And, with Zouma now waiting in the wings, the pair will know they have reliable backup.