The 29-year-old midfielder will join up with Derek McInnes’ squad on Thursday and could make his debut for the Robins when Blackpool visit Ashton Gate on Saturday.
Danns has made 40 appearances for Leicester since joining the Foxes in July 2011, but has featured just three times for the first team so far this season.
His loan spell with Bristol City will run up to Wednesday 12 December, making him available for the Robins’ next five games, including a further home game against Wolves, plus away trips to Middlesbrough, Brighton and Sheffield Wednesday.