The Irishman, 27, has signed a three-year contract at Ewood Park, where he will link up with former Dons boss Paul Ince for a second time.
Andrews started his career with Wolves, before scoring 21 goals in 87 appearances during his two seasons with the controversial Milton Keynes side.
"Coming here is a fantastic opportunity for me and it is one that I am really relishing and I hope to take with both hands," he said.
"I'm under no illusions, it is going to be a very hard test for me to get into the team, but it is one that I am relishing and very much looking forward to."