He succeeds Heyneke Meyer who opted not to make himself available for possible reappointment at the conclusion of his contract in December.
Coetzee, 52, has left his position as the head coach of Kobe Kobelco Steelers in Japan to join SA Rugby having previously been the head coach of the Stormers and Western Province.
He was previously an assistant to Jake White as part of the World Cup-winning 2007 Springbok team.
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