Austin was available on a free transfer after being released by Leeds United earlier this summer. He had been keen to sign for a club in England, but work permit complications meant he had been forced to look elsewhere.
The 30-year-old has signed for the Danish giants until the summer of 2017 and will be playing alongside former Liverpool defender Daniel Agger at the club.
Austin has been handed the number 8 shirt by Brondby, who are delighted to have secured his signature. "Rodolph is a winner. He demands a lot from himself and his team-mates, he is a guarantee of hard work and dedication, and he is good at using his physique", sporting director Troels Bech said on Brondby's official website.
"We are looking forward to seeing Rodolph in the Brondby midfield."
The club confirmed that they have started the process of applying for a work permit for Austin, after which time he can begin to train with his new team-mates.
Brondby currently sit fourth in the Danish Superliga with ten points from seven games.