The veteran striker is back at Stamford Bridge after a two-year absence, which saw him represent Shanghai Shenhua and Galatasaray.
Having linked up once again with Jose Mourinho, Drogba is focused on ensuring Chelsea claim their first domestic title since 2010.
"I'm not coming here to break records, I just want to win trophies," the 36-year-old Ivorian told the club's official website.
"Five years is a long time not to win the Premier League, so I want to win it.
"To lift the Premier League trophy is a fantastic feeling and we haven't experienced it for a few years - it's too long for a club like ours."
Drogba initially joined Chelsea in 2004 as one of Mourinho's first signings during the Portuguese's first stint at the Chelsea helm.
He went on to score 157 goals for the London club and the winning penalty as Chelsea defeated Bayern Munich in a shootout to win the 2011-12 UEFA Champions League.
"It's amazing to be back, a great feeling," Drogba added.
"It was an easy decision to make; it's very difficult to say no to Jose and to Chelsea.
"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 on the pitch.
"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."
