Springbok director of rugby, Rassie Erasmus and SA Rugby confirmed on Thursday that they will no longer contest the ban handed out by World Rugby's judicial committee earlier in November.
Both Erasmus and SA Rugby also apologised to match officials in control of the first Test of the Springboks' Series against the British & Irish Lions.
Erasmus was found guilty on all six charges brought against him after he compiled a 62-minute video in which he hit out at Australian referee Nic Berry's and TMO Marius Jonker's officiating during that match.
The ban means Erasmus is suspended from all rugby-related activities for two months, although he still had to serve a match day ban until 30 September 2022.
SA Rugby was fined £20 000 (around R418 000) and received a warning regarding future conduct.
In a statement sent to media on Thursday afternoon, SA Rugby confirmed that World Rugby had been advised over the withdrawal of the appeal.
"We have drawn a line under the incident and only wish to look forward. We will respect the outcomes of the hearing, allowing our national teams and rugby operations to plan with clarity for the coming months," the statement went on to say.
Read the full statement below:
"SA Rugby and Rassie Erasmus wish to apologise to the match officials appointed to the first Test of the Springboks' Series against the British & Irish Lions.
We also confirm that SA Rugby and Erasmus have advised World Rugby that they withdraw their Notice of Appeal and will not lodge an appeal against the sanctions imposed by the Judicial Committee.
This has been a highly stressful and charged environment with unusual pressures placed on all concerned and we have no wish to prolong that experience for anyone.
We have drawn a line under the incident and only wish to look forward. We will respect the outcomes of the hearing, allowing our national teams and rugby operations to plan with clarity for the coming months."