Assistant coach Yeo Jun-hyung, who had been temporarily put in charge of the US team, has also resigned and accepted a suspension.
"In addition to their resignations, both have accepted suspensions from US Speedskating through February 2014, which includes the ...Olympic Winter Games in Sochi, Russia," US Speedskating said.
Both Chun and Yeo were already suspended.
Chun was also being investigated following complaints about the South Korean's training methods and claims of verbal, physical and psychological abuse of skaters.
He has repeatedly denied the allegations.
US Speedskating said it expected an arbitration hearing, scheduled to begin on November 1, to be dismissed now that both coaches had resigned.
The scandal already swirling around the two coaches exploded following claims by skater Simon Cho that he was ordered to tamper with Canadian rival Olivier Jean's skate at last year's world team short-track championships in Poland.
Jean was unable to compete in the 5,000 metres relay final because the blade had been bent out of shape and Canada, with only three skaters instead of the permissible four, finished last.
US Speedskating said disciplinary proceedings against Cho, a bronze medallist at the 2010 Vancouver Olympics, had begun and expected a hearing before its appeals commission to be held soon.
Both Chun and Yeo denied ordering Cho to damage the Canadian's skate but admitted to knowing about tampering and failing to report the incident.
The short track season opens on October 19 with a World Cup event in Calgary.