The 24-year-old joined BVB from Saint-Etienne this summer and marked his first game for the club with three goals
The 24-year-old moved to Signal Iduna Park for a reported €13 million from Saint-Etienne earlier this summer and despite noting the greater quality of the Bundesliga, wasted little time in making an impression at his new club on Saturday.
''It is like a dream for me, an unbelievable feeling. I feel right in Dortmund,” he told Bild.
“The Bundesliga is much more intensive than the Ligue 1. Here you have much more tempo and I have to work in the defence, but it is okay.
"When we can continue our good work then we will have a great season. The first goal was something special for me and I wanted to celebrate it in a special way.''
Dortmund coach Jurgen Klopp then revealed his belief that Aubameyang can become even more dangerous in the months ahead, while defender Neven Subotic hailed the Gabon international's flawless first outing.
''He can do much more. He can hurt the opponents more,” Klopp said.
Subotic added: "It was a great example how you can have a perfect first game."
Dortmund next tackle Eintracht Braunschweig at home on October 19.