Mr Lindstrom said the pair stepped down because of the school's reaction to an incident involving two student rowers breaching security at Auckland Airport.
Jack Bell, 16, and Jordan Kennedy, 17, were caught riding on a baggage conveyor at the airport's domestic terminal while en route to the rowing regatta at Lake Karapiro last week.
While Mr Lindstrom notified school rector Justin Boyle that the boys - who were given formal warnings by police and the Aviation Security Service - would race, the decision was overridden, he said.
St Bede's, which yesterday confirmed Jack and Jordan's parents were not taking further legal action, did not provide comment on Mr Meates' and Mr Lindstrom's resignations.
A statement on its website from Mr Johnstone said the rowing team was welcomed back to the school on Monday.
"There are also support plans in place for all of the boys and staff as required.
"All students have been reminded of the need to support all of their peers whatever their own views may be and allow proper processes to be followed."
The board and rector would also not be making any comments to the media about the situation, Mr Johnstone said.
"The Board is unanimous in its view that the first priority remains the well-being of the boys and continued media coverage and social media debate is causing additional stress for many of the boys, their parents, other students and the wider St Bedes community."
Mr Spencer, Mr Johnstone and Mr Boyle could not be reached for comment.
