The Dortmund forward is eager to live up to his predecessor's impressive scoring record after replacing the Bayern Munich striker at Signal Iduna Park
Insgine, last season's top scorer in Serie A, completed his move to Dortmund from Torino in June as a replacement for Lewandowski, who has joined Bayern Munich.
The 24-year-old has urged the club's supporters to forget about the Poland international, who scored 103 goals in four seasons at Signal Iduna Park, and back him to fill the void in attack.
"Lewandowski is past, I am the future," said Immobile at a press conference.
"Lewandowski is a great player. I'll try to do my best. Then we will see if I can score more or less goals than him.
"I am very happy to have arrived at a big club. So far all expectations have been fulfilled here. [Head coach Jurgen] Klopp takes me often to the side, tells me that I should take it easy. I have a good feeling with the coach."
The Italian, who was part of his country's squad for the World Cup, also revealed that his team-mates have been helping him to learn German since his return from Brazil and that his first phrases were 'how are you?' and 'top scorer'.
Immobile added: "I would like to thank Sebastian Kehl and my interpreter. From them I got two notes with the most important coaching words. I must learn those for tomorrow."
Dortmund continue their pre-season preparations with a friendly against Chievo on Friday.