The 36-year-old Ivory Coast striker signed a 12-month deal last week to return to Stamford Bridge after having left the club immediately after their 2012 Champions League final victory over Bayern Munich.
"Five years is a long time not to win the Premier League so I want to win it," Drogba told the club website (www.chelseafc.com).
"To lift the Premier League trophy is a fantastic feeling and we haven't experienced it for a few years, too long for a club like ours.
"I missed the Premier League, which for me is the best in the world. It's true the German league is on the way up but the English league has been the best over the last decade and I'm really looking forward to playing the first game."
Drogba won the top-flight crown three times in his first spell at Chelsea, in 2005, 2006 and 2010, and also lifted the FA Cup four times and the League Cup twice.
"It's amazing to be back, a great feeling," he said. "I'm happy to be back here and I'm looking forward to seeing the best fans.
"It was an easy decision to make, it's very difficult to say no to (manager) Jose (Mourinho) and to Chelsea. I have so many good memories with the club."
Drogba, who has scored 157 goals in 341 appearances for Chelsea, was one of Mourinho's first signings when the Portuguese first joined the club in 2004.
"He said to me that a player like me, who has history with the club, should come back one day," said the Ivorian, who had short spells in China with Shanghai Shenhua and in Turkey with Galatasaray during his time away from Stamford Bridge.
"I agree with him because even if I left I was still a Chelsea player because of the eight years I spent here. No offence to the teams I was with during those two years but that's just the way it is.
"He's the one who gave me a chance to play in the Premier League. We won so many trophies together and so many matches," added Drogba, who will wear the same number 15 shirt he sported when he first joined Chelsea in 2004.
"His relationship is not only with me, it's with all the players who were here from the beginning of the story. It's quite emotional but the most important thing is that we want to win, win, win."
Chelsea, who finished third in Mourinho's first campaign back in charge last term, launch their new season at promoted Burnley on Aug. 18.
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- 2012 Champions League final