Amini amassed over 130 appearances for the club across four seasons but will now look to ply his trade elsewhere in 2020-21.
In one last act of generosity, the 27-year-old took to the streets of Aarhus alongside compatriot Zach Duncan to hand out a range of items to the community.
"I’ve been living here for four years and I see this area with the people, so I thought why not give them this stuff that I’m not going to take with me, and it was a hit, they were really happy," Amini told Socceroos.com.au.
"One of them actually teared up because he said it was his birthday and he got my suit which was so nice.
"He actually took off his shirt in the middle of the street and put it on which was funny."
The former Central Coast Mariners midfielder departs the Danish city having helped claim their first top-three finish in 23 years.