Emergency crews were called to the Moonarie climbing area in Wilpena Pound at about 1:15pm on Sunday, when the two Adelaide men did not return to their camp.
Police said the men — a 62-year-old from Norwood and a 44-year-old from Fairview Park — were later found dead in the area.
It is believed they fell to their deaths in what police described as "extremely remote" and "inaccessible terrain".
An operation to recover their bodies is expected to begin this morning.
Officers from SA Police Special Tasks and Rescue (STAR) are expected to fly to the area and be assisted by local patrols and State Emergency Service (SES) volunteers.
Police are investigating the men's deaths and will prepare a report for the coroner.
"The two guys involved — just amazing individuals and really unique [and] wonderful characters in the South Australian community as well, and they'll be sorely missed," experienced climber Rob Baker said.
The Climbing Club of South Australia also paid tribute to the victims on social media.
It said it "couldn't be more sad about the situation that has occurred".