The 30-year-old left Leeds this summer and has now completed a move to Denmark.
The Jamaica skipper was released by Leeds United over the summer but was not allowed to return to English football with Sheffield Wednesday after failing to receive a work permit. It is unclear whether that same ruling played a part in United's decision not to extend Austin's contract.
But the midfielder has now resolved his next move and Leeds wished him luck on Twitter after the switch was confirmed.
It appears the 30-year-old's first choice would have been to stay in England, with a campaign being set up online to help overturn the decision not to grant him a work permit.
That possibility is now over, though, and Leeds fans have also joined the club's official account in sending a message to Austin on social media.
Indeed, the reaction has largely been positive that the Jamaican's future is no longer up in the air - and many supporters are wishing him all the best ahead of the move. Here's how Leeds fans reacted to the Austin news on Twitter:
I love Rudy Austin always puts in big effort, hope he does well— LUCAS (@Baerardi) September 9, 2015
Great move for rudy austin hope it all works out for him may not have been yaya but he loved playing for us— Jake (@Jakerbomb_) September 9, 2015