Etzebeth took over as skipper when Whiteley sustained a groin injury during the Test series victory over France in June.
Etzebeth has been an inspiration since being installed as stand-in captain and the towering lock will continue to lead his country out.
Springboks head coach Allister Coetzee said: “Eben has really taken to his role as captain of the Springboks and it makes sense to retain him. I know he is well respected by talking to opposition coaches and referees, and he enjoys the respect of his peers.
“With Eben at the helm for the Castle Lager Outgoing Tour, we are looking forward to continue our process of building continuity, cohesion and experience within this team as we also start to build towards the 2019 Rugby World Cup in Japan.”