He'll be well known to Clarets boss Owen Coyle having played most of his career with Aberdeen. Coyle himself had said he was looking to strengthen his defensive options and Anderson does just that.
He is an experienced player who played almost 350 games for Aberdeen before moving south to the Stadium of Light in a £1 million deal in the summer of 2007.
He becomes our seventh signing since the end of last season and could even make his debut tonight in the Carling Cup tie against Oldham.
Manager Owen Coyle said: "We are delighted to add Russell to the squad. We have been chasing him for a while, but obviously the finances involved, along with a couple of other things, did not make it possible until now.
"He is a player I have full admiration for. I remember him at Aberdeen where he was held in such high esteem that Sunderland eventually paid £1 million for his services.
"Unfortunately he had no sooner signed than he picked up an injury and obviously he ended up finding it hard to get back into Roy Keane's side. But there is no doubting the quality he has. We have seen him at close quarters and he did well on loan at Plymouth last season and he will be a tremendous acquisition."