The 36-year-old has been training with Rovers since leaving the Black Cats in the summer
A deal had been delayed by a calf injury Brown suffered during pre-season
The former England international will also spend time working with Damien Johnson and David Dunn coaching the club's Under-23 side
Blackburn boss Owen Coyle has praised Brown's attitude during training, saying on Tuesday night: "He's been outstanding
He's a constant professional - his attitude has been exemplary around the training ground with the young players, helping and encouraging them."
Source : PA