Dortmund coach Jurgen Klopp moved for Immobile and Adrian Ramos to bolster his forward line after Lewandowski's free transfer move to bitter rivals Bayern Munich.
Immobile was the leading scorer in Serie A last season with 22 goals during a loan spell with Torino, a campaign that saw him earn an Italy call-up and feature at the World Cup.
Prior to the tournament in Brazil the 24-year-old agreed a switch from parent club Juventus to the Bundesliga and will be hoping to lead the line in the absence of Lewandowski.
The Poland international will be a tough man to replace after his impressive tally of 103 goals in 187 appearances but Immobile, with the support of Klopp, is confident he can adapt to a new style of play in Germany.
"He's [Klopp] trying to tell me things little by little," he said at a media conference on Thursday. "This is a new way to play football and certainly a change.
"The workouts are different and the training intensity is higher than my former club. But this is expected because we're playing in three competitions.
"He [Lewandowski] is a great player, so I'll try to do my best and we will see whether I succeed to achieve a similar goal.
"Robert is the past, I am the future."
Immobile netted his first Dortmund goal in their latest pre-season clash with Rot-Weiss Essen on Sunday, when he rounded off a 5-1 win.
