The 18-year-old with a distinctive bright Afro hairstyle would remain on loan to the Mariners until May next year before crossing to Germany, the club said on its website.
"I'm really excited to be joining Dortmund, they're a big club with amazing supporters," said Amini, who trained with Dortmund earlier this year.
Amini, who will play in the Under-20 World Cup in Colombia starting on July 29, said he would use his first payment from Dortmund to buy his parents a television set with European sports channels to allow them to watch him overseas.
"A big screen television would be a nice way of paying them back and showing them how grateful I am," he told local broadcaster SBS.
