Brown played 16 games in six seasons for Rovers although he did go out on loan to a number of clubs.
But Brown wanted to feel settled at a club and he liked what Dons manager Craig Brown had to say to him about joining the club.
Brown said: "I have worked with Archie at Blackburn and spoke to the manager.
"His passion and Archie's passion in terms of trying to achieve something up here and in terms of trying to bring me in, it was refreshing.
"They showed great ambition and I thought, 'most definitely, I'll come and give it a go'."