The 34-year-old defender has made 26 appearances this season, moving on from the injury problems that often undermined his spell in England with Sunderland and Derby.
Anderson told the club's official website: "I've always said the day I don't feel up for the rigours of the SPL, I'll stop there and then but right now, I'm as fit as I have been and I'm really looking forward to at least another year playing.
"I started my career at Aberdeen and it's fitting that I'll finish my playing career here as well."
Aberdeen chief executive Duncan Fraser added: "Russell's influence both on and off the park is absolutely immense and he is a club captain in the true sense of the word.
"He has always said he wants to carry on playing for as long as he feels able to do so and everyone at the Club is delighted for him."