He, along with team mate Moises Henriques, will fly to South Africa on Friday.
There was no such immediate joy for Marsh, who injured his calf during Australia's one-day series against England and was undergoing treatment at Perth.
After the first test in Centurion, Port Elizabeth will host the second from February 20 while Cape Town is the venue for the third and final test from March 1.
(Reporting by Amlan Chakraborty; editing by Sudipto Ganguly)