General Meiring, 58, who did not admit any wrongdoing, said he was stepping down "without prejudice" and would seek his pension.
President Nelson Mandela said he accepted the resignation "with regret" and that he had agreed to allow General Meiring to retire early.
General Siphiwe Nyanda, a former anti-apartheid guerrilla and General Meiring's understudy in recent months, is considered his likely successor.
He was one of several military and government officials named in a report that General Meiring gave Mr Mandela on 5 February. The report alleged that members of the ruling African National Congress were involved in a plot to topple the government.
Mr Mandela says he never believed the report, while some government officials said it was part of a disinformation campaign by apartheid-era elements in the military. On 27 March, Mr Mandela appointed a commission to investigate how the report was compiled.
In his statement, General Meiring said he was resigning because he was responsible for turning over "uncorroborated" evidence to the President.
Jakes Gerwel, Mr Mandela's chief-of-staff, said the President considered General Meiring's decision "appropriate and honourable." He said the government planned no further investigation of the report, which he called "laughable and ridiculous."Reuse content