Brown played 16 games in six seasons with Rovers and spent time on loan at Leeds, Cardiff and Leyton Orient last season.
The 29-year-old has signed a two-year contract after being encouraged by the enthusiasm of Dons manager Craig Brown and assistant Archie Knox.
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'."
Brown hopes to revive his international career by playing first-team football after being frustrated at Blackburn.
With Jamie Langfield still recovering from a brain seizure, Brown will initially be understudy to on-loan Manchester City player David Gonzalez.
But he hopes to force himself into the first team after building up his sharpness.
"Without a doubt, that's the reason I came," he said. "I'm bringing my family up, I have come here to play football.
"I have not come here to sit on the bench. I have maybe been unfortunate in one or two instances at Blackburn.
"Brad Friedel was probably a freak of nature, he showed unbelievable consistency.
"Paul Robinson came in with a big reputation and he has played well. So I have not played as many games as I would have liked.
"All I can do is get myself in the best shape I can over the next couple of weeks and get training with the boys and try and play some games."
Source: Team Talk
Source: Team Talk