The 25-year-old international was allegedly stopped by police several times and received speeding tickets on at least five occasions since 2011 before authorities realised he had been driving without a licence ever since.
"I decided back then to take that road but the reasons I did it are something I cannot really understand today," Reus was quoted as saying in the German paper.
Dortmund's prosecutor's office said the fine was 540,000 euros (£426,814) related to incidents from 2011 until this March.
"Today I know that I was too naive and that it was stupid. I have learned my lesson and this will not happen again," Reus said.
The club could not be immediately reached for a comment.
Reus, who missed Germany's World Cup triumph in July after picking up an injury in the final warmup game, is a transfer target of several major European clubs.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
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