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.
In a statement, World Rugby said: "World Rugby welcomes the public apology from SA Rugby and Rassie Erasmus to the match officials involved in the first test between South Africa and the British & Irish Lions this year and the matter is closed."