Faingaa, 29, started his career in Canberra before moving to Brisbane to help the Reds to their 2011 Super Rugby triumph and earning 36 caps for Australia.
"With Stephen Moore returning to the Reds next year there was obviously a gap we needed to fill in our squad and I think Saia is a perfect fit," said Brumbies coach Stephen Larkham.
"His aggression, low tackles and fervour at the breakdown will definitely be of great benefit to us next season."
If Faingaa's centre brother Anthony, who also plays for the Reds and has been capped for Australia, does not follow Saia south then the twins will be separated for the first time since they started playing the game as five-year-olds for the Queanbeyan Kangaroos.
(Reporting by Nick Mulvenney, editing by Ian Ransom)
