The Ivory Coast striker is back at Stamford Bridge after signing a one-year deal last month.
Drogba, 36, scored 157 goals in 342 games in his first spell with the club, which spanned eight years.
Terry, 33, told Chelsea TV: "Didier's still the same. He's been a nightmare to play against in training. He's still strong, sharp and hungry."
Chelsea have signed Diego Costa,Cesc Fabregas and Filipe Luis at a combined cost of £75m this summer.
In addition to Drogba's arrival after he left Turkish side Galatasaray, defender Kurt Zouma and goalkeeper Thibaut Courtois have returned to Chelsea after loan spells.
Former England captain Terry added: "It's important Didier is here because he brings that mentality of wanting to win every day.
"That rubs off on people like Kurt Zouma and the other young players.
"It's time for these players to continue to keep winning trophies for this club and keep the fans and owner happy.
"If I was a Chelsea fan I'd be impressed from what I have seen so far from Diego, Cesc, Filipe and all the boys that have come in like Kurt as well."
Terry admits it feels strange to see former Stamford Bridge team-mates Frank Lampard and Ashley Cole playing for new clubs this season.
Lampard has joined Manchester City, with former England defender Cole signing for Italian club Roma. Terry added:  "It just doesn't seem right to see them in different shirts."
John Terry has backed Chelsea team-mate Didier Drogba to be a success on his return to the Premier League.