The 24-year-old striker made a £54 million switch from RB Leipzig earlier this summer, and he has described the transfer as a "little dream".
He said: "We talked a lot about the system, how he [Lampard] wants to play and sees me playing. He knows me now a little bit better and it fits very good between us...
"When you have a decision to go from your old club and you come to a big club like this, it was for me a dream which came true because Chelsea is a very big club.
"I know of the players before when they won the Champions League with [Didier] Drogba, with my new manager Frank Lampard, Petr Cech as the technical advisor, it is like a little dream for me.
"But I want to become, not a same player like them, I want to be part of a new era here so I will play to try to give my best."
The German star is certain he can cope with the demands of the Premier League.
He's quoted by BBC Sport as saying: "The style of the Premier League is very fast and my speciality is that I am really fast so I think it is perfect for me to play here.
"It is another league in another country so I can improve myself to bring it to another level, so those are the reasons I come to the Premier League and to Chelsea."